Distinguishing simple algebras by means of polynomial identities

  • Yuri Bahturin
  • Felipe YasumuraEmail author


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.


Graded algebra Polynomial identity Universal algebra 

Mathematics Subject Classification

17A42 08B20 16R50 



We would like to thank you the anonymous referee for his/her comments on the exposition of this paper.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Instituto de Matemática e Estatística da Universidade de São Paulo 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada
  2. 2.Department of MathematicsUniversidade Estadual de MaringáMaringáBrazil

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