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The Haar measure of a profinite n-ary group J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-22 M. Shahryari, M. Rostami
We prove that every profinite n-ary group (G,f)=der𝜃,b(G,•) has a unique Haar measure mp and further for every measurable subset A⊆G, we have mp(A)=m(A)=(n−1)m∗(A), where m and m∗ are the normalized Haar measures of the profinite groups (G,•) and the Post cover G∗, respectively.
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On (naturally) semifull and (semi)separable semifunctors J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-20 Lucrezia Bottegoni
The notion of semifunctor between categories, due to [9], is defined as a functor that does not necessarily preserve identities. In this paper, we study how several properties of functors, such as fullness, full faithfulness, separability, natural fullness, can be formulated for semifunctors. Since a full semifunctor is actually a functor, we are led to introduce a notion of semifullness (and then
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On computing finite index subgroups of PSL2(ℤ) J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-20 Nicolás Mayorga Uruburu, Ariel Pacetti, Leandro Vendramin
We present a method to compute finite index subgroups of PSL2(ℤ). Our strategy follows Kulkarni’s ideas, the main contribution being a recursive method to compute bivalent trees as well as their automorphism groups. As a concrete application, we compute all subgroups of index up to 20. We then use this database to produce tables with several arithmetical properties.
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Left and right hybrid (b,c)-core inverses in semigroups with involution J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-20 Huihui Zhu, Chenxiang Hong, Dijana Mosić
Let S be a unital ∗-semigroup and let a,b,c∈S. The goal of this paper is to introduce two new classes of generalized inverses, called the left hybrid (b,c)-core inverse and the right hybrid (b,c)-core inverse. An element a∈S is left hybrid (b,c)-core invertible if there exists some x∈S such that caxc=c, 0x=0b and Sx=Sc∗. Such an x is called a left hybrid (b,c)-core inverse of a. Several criteria and
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Investigation of ID-derivations of finite-dimensional nilpotent Lie algebras J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-19 Seyed Mahdi Moosavinejad, Farshid Saeedi
Let L be a Lie algebra and let Der(L) be the set of all derivations of L. Then the derivation α of L is called an ID-derivation if α(x)∈L2 for all x∈L. The set of all ID-derivations is denoted by ID(L). Let Derz(L) be the set of all central derivations and let C∗(L) and ID∗(L) be, respectively, the set of all center derivations and ID-derivations that map Z(L) to zero. In this paper, we verify relations
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Cryptanalysis of a key exchange protocol based on a congruence-simple semiring action J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-19 A. Otero Sánchez, J. A. López Ramos
We show that a previously introduced key exchange based on a congruence-simple semiring action is not secure by providing an attack that reveals the shared key from the distributed public information for any of such semirings.
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Images of multilinear polynomials on generalized quaternion algebras J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-15 Peter V. Danchev, Truong Huu Dung, Tran Nam Son
In connection with the work of Malev published in [J. Algebra Appl.13 (2014) 1450004; J. Algebra Appl.20 (2021) 2150074], we continue to provide a classification of possible images of multilinear polynomials on generalized quaternion algebras.
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Abundance of the ideals of the monoid of all orientation-preserving extensive full transformations J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-13 Ping Zhao
Let 𝒪𝒫ℰn be the monoid of all orientation-preserving and extensive full transformations on {1,…,n}. In this paper, first we discuss left and right abundance of the principal ideals of 𝒪𝒫ℰn. Second, we give necessary and sufficient conditions for the principal ideals of 𝒪𝒫ℰn to be abundant and regular. Finally, we study abundance of the ideals in 𝒪𝒫ℰn.
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On finite groups with weakly σ-normal subgroups J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-11 Juping Tang, Jiuzhou Ji, Nanying Yang
Let G be a finite group and σ={σi|i∈I} some partition of the set of all primes. A subgroup H of G is said to be weaklyσ-normal in G if there exists a σ-subnormal subgroup T of G such that G=HT and H∩T≤H∗≤H, where H∗ is either σ-permutably embedded or σ-semipermutable in G. In this paper, we investigate the influence of weakly σ-normal subgroups on the structure of finite groups.
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The equation characterizations of generalized inverses in a ring with involution J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-06 Anqi Li, Junchao Wei
In this paper, we study the relation between the generalized inverse properties of an element in a ring with involution and related equations. Mainly, by exploring the existence of the solution in a given set and the expressions of the general solution to these constructed related equation, we obtain a lot of new characterizations of EP elements, partial isometries, SEP elements, Hermitian elements
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The proper class generated by τ-supplements J. Algebra Appl. (IF 0.8) Pub Date : 2024-03-02 Salahattin Özdemi̇r, Zübeyi̇r Türkoğlu
In this paper, we study supplement submodules with respect to a torsion class of any torsion theory, generalizing the concepts of sa-supplement, extended S-supplement, Rad-supplement submodules, etc. We give some homological properties of this class of modules, which forms a proper class, and use them to characterize some rings in terms of those certain modules.
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Lie centralizing mappings on generalized matrix algebras through two-sided zero products J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-28 Nurcan Argaç
Let 𝒰=AMNB be a generalized matrix algebra defined by the Morita context (A,B,M,N,ΦMN,ΨNM) and 𝒵(𝒰) the center of 𝒰. In this paper, under some certain conditions on 𝒰, we prove that if F:𝒰→𝒰 is an additive map satisfying [x,F(y)]=0 for any x,y∈𝒰 with xy=0=yx, then F has the form F(x)=λx+τ(x) for all x∈𝒰, where λ∈𝒵(𝒰) and τ is an additive map from 𝒰 into 𝒵(𝒰). Finally as its applications
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Para-Kähler and pseudo-Kähler structures on Lie–Yamaguti algebras J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-28 Jia Zhao, Yuqin Feng, Yu Qiao
For a pre-Lie–Yamaguti algebra A, by using its sub-adjacent Lie–Yamaguti algebra Ac, we are able to construct a semidirect product Lie–Yamaguti algebra via a representation of Ac. The investigation of such semidirect Lie–Yamaguti algebras leads us to the notions of para-Kähler structures and pseudo-Kähler structures on Lie–Yamaguti algebras, and also gives the definition of complex product structures
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Finite p-groups in which the cores of all the nonnormal subgroups are in the center J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-27 Libo Zhao, Yangming Li, Lü Gong, Xiuyun Guo
Let G be a finite p-group. Then G is said to be a CZ-group if HG≤Z(G) for every nonnormal subgroup H of G. In this paper, we study the CZ-group G and get c(G)≤3. It is proved that exp(G′)=p if c(G)=2 and |G|≤p5 if c(G)=3.
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On the schematicness of some Ore polynomials of higher order generated by homogenous quadratic relations J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-27 Andrés Chacón, Armando Reyes
In this paper, we investigate the property of schematicness introduced by Van Oystaeyen and Willaert [F. Van Oystaeyen and L. Willaert, Grothendieck topology, coherent sheaves and Serre’s theorem for schematic algebras, J. Pure Appl. Algebra104(1–3) (1995) 109–122] in the setting of skew Ore polynomials of higher order generated by homogenous quadratic relations defined by Golovashkin and Maksimov
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Relative Gorenstein flat modules and Foxby classes and their model structures J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-22 Driss Bennis, Rachid El Maaouy, J. R. García Rozas, Luis Oyonarte
We introduce the concepts of relative (strongly) cotorsion and relative Gorenstein cotorsion modules for a non-necessarily semidualizing module and prove that there exists a unique hereditary abelian model structure where the cofibrations are the monomorphisms with relative Gorenstein flat cokernel and the fibrations are the epimorphisms with relative cotorsion kernel belonging to the Bass class. In
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Deformations and abelian extensions of compatible pre-Lie superalgebras J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-21 Jamel Boujelben, Meher Abdaoui
In this paper, we give cohomologies and deformations theory, as well as abelian extensions for compatible pre-Lie superalgebras. Explicitly, we first introduce the notation of a compatible pre-Lie superalgebra and its representation. We also construct a new bidfferential graded Lie superalgebra whose Maurer–Cartan elements are compatible pre-Lie structures. We give the bidifferential graded Lie superalgebra
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Local and 2-local derivations of 𝔰𝔩(2) on any finite-dimensional completely reducible module J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-20 Shujuan Wang, Xiaomin Tang, Zhaoxin Li
This paper determines all local and 2-local derivations of the 3-dimensional complex simple Lie algebra 𝔰𝔩(2) on its any finite-dimensional completely reducible module. In particular, the quotient space of the one consisting of all local derivations by the one consisting of all derivations of 𝔰𝔩(2) on its (n+1)-dimensional simple module has the dimension n−1 if n is odd, and 0 otherwise. On the
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On the norm of the lower central series in a finite group J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-20 Lü Gong, Ziru Jing, Libo Zhao, Baojun Li
In this paper, the norm Li(G) of the lower central series in a finite group G is introduced, which unifies the norm of derived subgroups and nilpotent residuals. Some propositions of Li(G) are obtained, and some related subgroups as well as their equivalent propositions can also be found.
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Quandles with one nontrivial column J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-19 Nicholas Cazet
The axioms of a quandle imply that the columns of its Cayley table are permutations. This paper studies quandles with exactly one non-trivially permuted column. Their automorphism groups, quandle polynomials, (symmetric) cohomology groups, and Hom quandles are studied. The quiver and cocycle invariant of links using these quandles are shown to relate to linking number.
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On commuting automorphisms of finite p-groups of coclass 3 J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-16 N. Azimi Shahrabi, M. Akhavan-Malayeri
Let G be a group. If the set 𝒜(G)={α∈Aut(G):xα(x)=α(x)x for all x∈G} forms a subgroup of Aut(G), then G is called 𝒜-group. Recently, it has been proven that the minimum coclass of a non-𝒜p-group is equal to 3. In this paper, we deal with finite p-groups of coclass 3. We prove that a finite p-group G of order pn, n≥6, of coclass 3 for an odd prime p is an 𝒜-group except when the nilpotency class
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Products of commutators in certain rings J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-16 Tran Nam Son, Truong Huu Dung
Let R be a ring. For each positive integer k, [R,R]k (respectively, [R,R]≤k) is denoted by the set of all products of (respectively, at most) k additive commutators of R. If R is an algebra over a field F such that [R,R]k⊆F for some k, then [R,R]k={0}. If R is a noncommutative ring such that [R,R]k≠{0} for some k, then the necessary and sufficient condition for R to be a division ring is that every
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On finite groups with some Hall normally embedded subgroups J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-16 Wei Meng, Jiakuan Lu
Let G be a finite group. A subgroup H of G is called Hall normally embedded in G if H is a Hall subgroup of HG, where HG is the normal closure of H in G, that is, the smallest normal subgroup of G containing H. A group G is called a PHN-group if its all minimal subgroups and cyclic subgroup of order 4 are Hall normally embedded in G. In this paper, we give the classification of minimal non-PHN-groups
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Nil clean graphs associated with commutative rings J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-15 Moloukkhatoon Bozorgzadeh, Hosein Fazaeli Moghimi, Mahdi Samiei
Let R be a commutative ring with identity and Nil(R) be the set of all nilpotent elements of R. The nil clean graph of R, denoted by N.G(R), is a graph whose vertices are all nonzero nil clean elements of R and two distinct vertices x and y are adjacent if and only if xy∈Nil(R) or x−y∈Nil(R). In this paper, we focus on N.G2(R), the subgraph of N.G(R) induced by the set N.G2(R)={(e,n):0,1≠e∈Id(R)andn∈Nil(R)}
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Representations and cohomologies of differential 3-Lie algebras with any weight and applications J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-15 Qinxiu Sun, Zhen Li, Shan Chen
The purpose of this paper is to study cohomologies of differential 3-Lie algebras with any weight and applications. First, we introduce representations of differential 3-Lie algebras. Moreover, we develop cohomology theory of differential 3-Lie algebras. We also depict the relationship between the cohomologies of a differential 3-Lie algebra and its associated differential Leibniz algebra with weight
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On S-valuation domains J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-15 Dong Kyu Kim, Jung Wook Lim
Let D be an integral domain and let S be a multiplicative subset of D. In this paper, we study integral domains whose quotient rings are valuation domain. To do this, we introduce the concept of S-valuation domains. We define D to be an S-valuation domain if for each nonzero a,b∈D, there exists an element s∈S such that a divides sb or b divides sa. Among other things, we show that D is an S-valuation
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On a class of permutation quadrinomials J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-14 Zhiguo Ding, Michael E. Zieve
For each prime power q, we determine all a 𝜖 𝔽q2 for which X+Xq+X2q−1+aXq2−q+1 permutes 𝔽q2.
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Variations of primeness of ideals in rings of continuous functions J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-14 A. R. Aliabad, M. Ghoulipour, M. Paimann
In this paper, we describe some different variations of prime ideals in the context of rings of continuous functions such as strongly prime ideals, almost prime ideals, n-absorbing ideals, and 2-prime ideals. We characterize the strongly prime ideals of C(X). We prove that an ideal I of C(X) is almost prime if and only if it is semiprime or equivalently if and only if it is an (m,n)-closed ideal, where
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Fusion rules for the fixed point subalgebra of the vertex algebra associated with a non-degenerate and non-positive definite even lattice by an automorphism of order 2 J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-14 Kenichiro Tanabe
Let VL be the vertex algebra associated with a non-degenerate and non-positive definite even lattice L and VL+ the fixed point subalgebra of VL under the action of the automorphism induced from the −1-isometry of L. We determine the fusion rules for weak VL+-modules. As an application of this result, we classify the irreducible weak modules for the fixed point subalgebra of VL under the action of the
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Lambda number of the enhanced power graph of a finite group J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-14 Parveen, Sandeep Dalal, Jitender Kumar
The enhanced power graph of a finite group G is the simple undirected graph whose vertex set is G and two distinct vertices x,y are adjacent if x,y∈〈z〉 for some z∈G. An L(2,1)-labeling of graph Γ is an integer labeling of V(Γ) such that adjacent vertices have labels that differ by at least 2 and vertices distance 2 apart have labels that differ by at least 1. The λ-number of Γ, denoted by λ(Γ), is
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Almost Cohen–Macaulay bipartite graphs and connected in codimension two J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-14 Amir Mafi, Dler Naderi
In this paper, we study almost Cohen–Macaulay bipartite graphs. In particular, we prove that if G is an almost Cohen–Macaulay bipartite graph with at least one vertex of positive degree, then there is a vertex of deg(v)≤2. In particular, if G is an almost Cohen–Macaulay bipartite graph and u is a vertex of degree one of G and v its adjacent vertex, then G∖{v} is almost Cohen–Macaulay. Also, we show
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Directed partial orders on complex numbers and quaternions J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-14 Jingjing Ma
Let D be an integral domain that is algebraic over ℤ. It is shown that each directed maximal partial order on D is an Archimedean total order. Let F be a subfield of ℝ and C=F(i) be the complex field over F. As a consequence of the above result, if F is algebraic over ℚ, then C does not have a directed partial order making it a partially ordered ring. In particular, C cannot be a lattice-ordered ring
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Modularity conditions in Leibniz algebras J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-14 Pilar Páez-Guillán, Salvatore Siciliano, David A. Towers
In this paper, we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by the elements with square zero. We also study Leibniz algebras in which every subalgebra is a weak quasi-ideal, as well as modular symmetric Leibniz algebras.
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Hilbert coefficients of good I-filtrations of modules J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-14 Le Xuan Dung
Let M be a finitely generated module of dimension d over a Noetherian local ring (A,𝔪) and I an 𝔪-primary ideal. Let be a pair of good I-filtrations 𝔽 and 𝔽′ of M. We show that the Hilbert coefficients ei(𝔽) are bounded below and above in terms of i, e0(𝔽′),…,ei(𝔽′), and reduction numbers of 𝔽 and 𝔽′, for all i≥1.
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Cohomology and deformation theory of crossed homomorphisms of Leibniz algebras J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-14 Yizheng Li, Dingguo Wang
In this paper, we construct a differential graded Lie algebra whose Maurer–Cartan elements are given by crossed homomorphisms on Leibniz algebras. This allows us to define cohomology for a crossed homomorphism. Finally, we study linear deformations, formal deformations and extendibility of finite order deformations of a crossed homomorphism in terms of the cohomology theory.
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On the graded-Gelfand commutative rings J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-05 Mohamed Aqalmoun
This paper deals with the graded commutative rings in which every graded prime ideal is contained in a unique graded-maximal ideal called graded-Gelfand ring. The purpose is to establish some topological and algebraic characterizations of these rings, one of which is the algebraic analogue of Urysohn’s lemma. Finally, we look at a special class of those graded rings called graded-ordered rings which
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Modules and abelian groups with a restricted domain of projectivity J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-05 Rafail Alizade, Damla Dede Sipahi
In this paper, we study the modules whose projectivity domains are contained in the class of all pure-split modules and call them p-impecunious modules. Every quotient of a p-impecunious R-module is p-impecunious if and only if R is right pure semisimple. An abelian group A is p-impecunious if all p-components of A are nonzero and Bp(A)≠0 for some prime p where Bp(A) is the basic subgroup of the p-component
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Morita equivalences on Brauer algebras and BMW algebras of simply-laced types J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-05 Shoumin Liu
The Morita equivalences of classical Brauer algebras and classical Birman–Murakami–Wenzl (BMW) algebras have been well studied. Here, we study the Morita equivalence problems on these two kinds of algebras of simply-laced type, especially for them with the generic parameters. We show that Brauer algebras and BMW algebras of simply-laced type are Morita equivalent to the direct sums of some group algebras
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Inverse limits of automorphisms of truncated polynomials and applications related to Jacobian conjecture J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-05 Hao Chang, Bin Shu, Yu-Feng Yao
In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic p. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism φ of the polynomial ring k[x1,…,xn], if φ preserves the maximal ideals, then φ is an automorphism.
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When are ∨-additive mappings multiplicative? J. Algebra Appl. (IF 0.8) Pub Date : 2024-02-05 Noômen Jarboui, Bana Al Subaiei
In the spirit of some earlier studies of the authors, we discuss the alienation problem for ∨-additive and multiplicative mappings. This study enables us to answer two questions that were left open in [B. Al Subaiei and N. Jarboui, On the monoid of unital endomorphisms of a Boolean ring, Axioms10(4) (2021) 305].
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Zero product determined of amalgamated duplication of Banach algebras J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-31 M. Essmaili, R. Rajaenejad
In this paper, we study some sufficient and necessary conditions for the amalgamated duplication Banach algebra X⋊B to be zero product determined. Precisely, we show that in the case where X has a bounded approximate identity, X⋊B is zero product determined if and only if B is zero product determined and X⋊B has the property 𝔹. Moreover, we give a better characterization when X is unital. As an application
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On the structure and classification of Bernstein algebras J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-31 G. Militaru
Linear algebra tools are used to give a new approach to the open problem of the classification of Bernstein algebras. We prove that any Bernstein algebra (A,ω) is isomorphic to a semidirect product N⋉(⋅,Ω)k associated to a commutative algebra (N,⋅) such that (x2)2=0, for all x∈N and an idempotent endomorphism Ω=Ω2∈Endk(N) of N satisfying two compatibility conditions. The set of types of (1+|I|)-dimensional
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Twisted representations of ℕ-graded vertex algebras over a good field J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-31 Chao Yang
Let V be an ℕ-graded vertex algebra over a field 𝔽, and let g be an automorphism of V with a finite order T. Assume that the field 𝔽 contains a Tth primitive root of unity. We construct two associative algebras, Ag(V) and Rg(V), and investigate their properties and interconnections. As applications, we establish the following results: (1) If Rg(V) is finite-dimensional, then Ag(V) is also finite-dimensional;
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Jordan derivations on triangular algebras and trivial extensions J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-31 Maryam Ahsani, Mohammad Ramezanpour
In this paper, we provide a necessary and sufficient condition for a class of trivial extensions so that each Jordan derivation on such algebras can be written as the sum of a derivation and an antiderivation. Among other things, we obtain some of the known results concerning the Jordan derivations on trivial extensions with fewer assumptions. Also, as a generalization of a well-known result on triangular
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Certain linear isomorphisms for hyperalgebras relative to a Chevalley group J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-31 Yutaka Yoshii
Let G be a simply connected and simple algebraic group defined and split over a finite prime field 𝔽p of p elements. In this paper, using an 𝔽p-linear map splitting Frobenius endomorphism on a hyperalgebra relative to G, we obtain some 𝔽p-linear isomorphisms induced by multiplication in the hyperalgebra.
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Zassenhaus filtrations and right-angled Artin groups J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-31 Nguyên Thị Trà
We determine the restricted Lie algebra associated with the Zassenhauss filtration of a right-angled Artin group. We also provide another proof for a result of Koberda saying that the graph is uniquely determined by the first and second cohomology groups, together with the cup product, of the associated right-angled Artin group.
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Rings with S-Noetherian spectrum J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-31 Ahmed Hamed, Hwankoo Kim
Let R be a commutative ring with identity and S be a multiplicative subset of R. We say that R has S-Noetherian spectrum if for every ideal I of R,sI⊆J⊆I for some s∈S and some finitely generated ideal J. In this paper, we study rings with S-Noetherian spectrum. Among other things, we give a necessary and sufficient condition for Nagata’s idealization R(+)M, where M is an R-module, to satisfy the S-Noetherian
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The set of representatives and explicit factorization of xn − 1 over finite fields J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-29 Manjit Singh, Deepak
Let n be a positive integer and let 𝔽q be a finite field with q elements, where q is a prime power and gcd(n,q)=1. In this paper, we give the explicit factorization of xn−1 over 𝔽q and count the number of its irreducible factors for the following conditions: n,q are odd and rad(n)|(q2+1). First, we present a method to obtain the set of all representatives of q-cyclotomic cosets modulo m, where m=gcd(n
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Weak Hopf algebras, smash products and applications to adjoint-stable algebras J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-24 Zhimin Liu, Shenglin Zhu
For a semisimple quasi-triangular Hopf algebra (H,R) over a field k of characteristic zero, and a strongly separable quantum commutative H-module algebra A, we show that A#H is a weak Hopf algebra, and it can be embedded into a weak Hopf algebra EndA∗⊗H. With these structures, A#HMod is the monoidal category introduced by Cohen and Westreich, and EndA∗⊗Hℳ is tensor equivalent to Hℳ. If A is in the
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Cohomology of modified Rota–Baxter Leibniz algebra of weight λ J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-24 Bibhash Mondal, Ripan Saha
Rota–Baxter operators have been paid much attention in the last few decades as they have many applications in mathematics and physics. In this paper, our object of study is modified Rota–Baxter operators on Leibniz algebras. We investigate modified Rota–Baxter Leibniz algebras from the cohomological point of view. We study a one-parameter formal deformation theory of modified Rota–Baxter Leibniz algebras
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Free Ω-Rota–Baxter systems and Gröbner–Shirshov bases J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-24 Yuanyuan Zhang, Huhu Zhang, Xing Gao
In this paper, we propose the concept of an Ω-Rota–Baxter system, which is a generalization of a Rota–Baxter system and an Ω-Rota–Baxter algebra of weight zero. In the framework of operated algebras, we obtain a linear basis of a free Ω-Rota–Baxter system for an extended diassociative semigroup Ω, in terms of bracketed words and the method of Gröbner–Shirshov bases. As applications, we introduce the
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Tropical matrix groups and Boolean matrix groups J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-24 Lin Yang, Miao-Miao Ren, Ling-Li Zeng
In this paper, we give a complete description of the maximal subgroups of the semigroup of all n×n tropical matrices under multiplication up to isomorphism. Using the description, we prove that every subgroup of the semigroup of all n×n Boolean matrices under multiplication is embedded in the symmetric group Sn.
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Partial actions of Sweedler Hopf algebra on generalized quaternion algebra J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-19 Yong Deng, Quanguo Chen, Dingguo Wang
In the paper, we discuss the partial actions of Sweedler Hopf algebra on the generalized quaternion algebra, and give the sufficient and necessary conditions to make the actions be the partial actions. As an application, we give a complete description of all partial actions of Sweedler Hopf algebra on the generalized quaternion algebra.
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Arithmetic of semisubtractive semidomains J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-19 Hannah Fox, Agastya Goel, Sophia Liao
A subset S of an integral domain is called a semidomain if the pairs (S,+) and (S∖{0},⋅) are commutative and cancellative semigroups with identities. The multiplication of S extends to the group of differences 𝒢(S), turning 𝒢(S) into an integral domain. In this paper, we study the arithmetic of semisubtractive semidomains (i.e. semidomains S for which either s∈S or −s∈S for every s∈𝒢(S)). Specifically
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Kostant’s generating functions and Mckay–Slodowy correspondence J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-19 Naihuan Jing, Zhijun Li, Danxia Wang
Let N⊴G be a pair of finite subgroups of SL2(ℂ) and V a finite-dimensional fundamental G-module. We study Kostant’s generating functions for the decomposition of the SL2(ℂ)-module Sk(V) restricted to N◃G in connection with the McKay–Slodowy correspondence. In particular, the classical Kostant formula was generalized to a uniform version of the Poincaré series for the symmetric invariants in which the
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A look at FPF rings J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-18 E. Ghashghaei, M. Tamer Koşan, T. Cong Quynh, L. Van Thuyet
An error in Corollary 9.32 of [C. Faith, Rings and Things and a Fine Array of Twentieth Century Associative Algebra, Mathematical Surveys and Monographs, Vol. 65 (American Mathematical Society, Providence, RI, 2004)], motivated us to consider again FPF rings which were initiated by Faith in the 1970s. In this paper, it is shown that a commutative ring R is reduced FPF if and only if it is Π-semihereditary
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A type C study of Braverman–Gaitsgory–Ginzburg’s construction of sln representations J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-12 Zhijie Dong, Haitao Ma
In [Z. Fan, H. Ma and H. Xiao, Equivariant K-theory approach to ı-quantum groups, Publ. Res. Inst. Math. Sci.58 (2022), no.3, 635–668], it is proved that the convolution algebra of the top Borel–Moore homology on the Steinberg variety of type B/C realizes U(sln𝜃), where sln𝜃 is the fixed point subalgebra of involution on sln. So, the top Borel–Moore homology of the partial Springer fibers gives the
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On finite groups in which every non-nilpotent maximal invariant subgroup is normal J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-12 Jiangtao Shi, Yifan Liu
Let A and G be finite groups such that A acts coprimely on G by automorphisms, we prove that if every non-nilpotent maximal A-invariant subgroup of G is normal, then G is p-nilpotent or p-closed for each prime divisor p of |G|, which improves a theorem obtained by Beltán and Shao.
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Window code parameters of spatially-coupled LDPC codes J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-11 Emily McMillon, Christine A. Kelley
In this paper, we define a window code to be the portion of a Spatially-coupled low-density parity check (SC-LDPC) code seen by a single iteration of a windowed decoder. We consider the design of SC-LDPC codes for windowed decoding via optimization of the window code. In particular, because iterative decoding is optimal on codes with cycle-free graph representations, we ask fundamental questions about
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Two results on character codegrees J. Algebra Appl. (IF 0.8) Pub Date : 2024-01-10 Yang Liu, Yong Yang
Let G be a finite group and Irr(G) be the set of irreducible characters of G. The codegree of an irreducible character χ of the group G is defined as cod(χ)=|G:ker(χ)|/χ(1). In this paper, we study two topics related to the character codegrees. The first result is related to the prime graph of character codegrees and we show that the codegree prime graphs of several classes of groups can be characterized