Distinguishing simple algebras by means of polynomial identities
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Our main goal is to extend one of classical Razmyslov’s Theorem saying that any two simple finite-dimensional \(\Omega \)-algebras over an algebraically closed field, satisfying the same polynomial identities, are isomorphic. We suggest a method that allows one to reduce problems about identities of algebras with additional structure to the identities of \(\Omega \)-algebras. For the convenience of the reader, we start with a full detailed proof of Razmyslov’s Theorem. Then we describe our method and its consequences for the identities of graded algebras, algebras with involution, and several others.
KeywordsGraded algebra Polynomial identity Universal algebra
Mathematics Subject Classification17A42 08B20 16R50
We would like to thank you the anonymous referee for his/her comments on the exposition of this paper.
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On behalf of all authors, the corresponding author states that there is no conflict of interest.
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