Skip to main content
SpringerLink
Log in

Schauffler-Type Theorems

  • Published:
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) Aims and scope Submit manuscript

Abstract

In this work the Belousov theorem on linearity of invertible algebras with the Schauffler \(\forall\exists(\forall)\)-identity is extended to regular division algebras for other associative \(\forall\exists(\forall)\)-identities. For the formulas at consideration, the Schauffler-type theorems are also proved. The results are applicable in cryptography (cf. [1–3]).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  1. R. Schauffler, ‘‘Eine Anwendung zyklischer Permutationen and ihre Theorie,’’ PhD Thesis (Marburg Univ., 1948).

  2. R. Schauffler, ‘‘Über die Bildung von Codewörtern,’’ Arch. Elektr. Übertragung 10, 303–314 (1956).

  3. R. Schauffler, ‘‘Die Associativität im Ganzen, besonders bei Quasigruppen,’’ Math. Z. 67, 428–435 (1957). https://doi.org/10.1007/BF01258874

    Article  MathSciNet  MATH  Google Scholar 

  4. V. D. Belousov, ‘‘Globally associative systems of quasigroups,’’ Mat. Sb., N.S. 55 (2), 221–236 (1961).

  5. Yu. Movsisyan, Hyperidentities: Boolean and De Morgan Structures (World Scientific, 2022). https://doi.org/10.1142/12796

  6. Yu. Movsisyan, Introduction to the Theory of Algebras with Hyperidentities (Yerevan State Univ. Press, Yerevan, 1986).

    MATH  Google Scholar 

  7. Yu. Movsisyan, Hyperidentities and Hypervarieties in Algebras (Yerevan State Univ. Press, Yerevan, 1990).

    MATH  Google Scholar 

  8. Yu. M. Movsisyan, ‘‘On a theorem of Schauffler,’’ Math. Notes 53, 172–179 (1993). https://doi.org/10.1007/BF01208322

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Davidov, A. Krapež, and Yu. Movsisyan, ‘‘Functional equations with division and regular operations,’’ Asian-Eur. J. Math. 11 (3), 1–14 (2018). https://doi.org/10.1142/S179355711850033X

    Article  MATH  Google Scholar 

  10. A. A. Albert, ‘‘Quasigroups I,’’ Trans. Am. Math. Soc. 54, 507–519 (1943). https://doi.org/10.1090/S0002-9947-1943-0009962-7

    Article  MATH  Google Scholar 

  11. A. A. Albert, ‘‘Quasigroups II,’’ Trans. Am. Math. Soc. 55, 401–419 (1944). https://doi.org/10.1090/S0002-9947-1944-0010597-1

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Krapež, ‘‘Generalized associativity on groupoids,’’ Publ. Inst. Math. (Beograd), N.S. 28 (48), 105–112 (1980).

Download references

Funding

The first author was partially supported by the Science Committee of Funding of the Republic of Armenia, project nos. 10-3/1-41 and 21T-1A213.

Author information

Authors and Affiliations

  1. Yerevan State University, Yerevan, Armenia

    Yu. M. Movsisyan & D. N. Harutyunyan

Authors
  1. Yu. M. Movsisyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. N. Harutyunyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yu. M. Movsisyan or D. N. Harutyunyan.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by E. Oborin

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Movsisyan, Y.M., Harutyunyan, D.N. Schauffler-Type Theorems. J. Contemp. Mathemat. Anal. 58, 116–124 (2023). https://doi.org/10.3103/S1068362323020073

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068362323020073

Keywords:

Search

Navigation