Abstract
In 1974 Kharchenko proved that if a \( 0 \)-component of an \( n \)-graded associative algebra is PI then this algebra is PI. In the Novikov algebras of characteristic 0 the existence of a polynomial identity is equivalent to the solvability of the commutator ideal. We study a \( 𝕑_{2} \)-graded Novikov algebra \( N=A+M \) and prove that if the characteristic of the basic field is not 2 or 3 and its 0-component \( A \) is associative or Lie-nilpotent of index 3 then the commutator ideal \( [N,N] \) is solvable.
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The work was supported by the Fundamental Research Program of the Russian Academy of Sciences (Project FWNF–2022–0002).
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Panasenko, A.S., Zhelyabin, V.N. Novikov \( 𝕑_{2} \)-Graded Algebras with an Associative 0-Component. Sib Math J 65, 426–440 (2024). https://doi.org/10.1134/S0037446624020150
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DOI: https://doi.org/10.1134/S0037446624020150