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In this paper we study the structure of a class of baric algebras satisfying the identity \( x^{2}x^{3}= (1-\alpha )\omega (x)^{2}x^{3}+ \alpha \omega (x)^{3}x^{2}\) where \(\alpha \in [0;1]\) . Using the Peirce decomposition we establish the links between this class of algebras and other classes such as Bernstein algebras, power-associative algebras, Jordan algebras, principal train algebras and evolution algebras.

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Structure of Algebras Satisfying an \(\omega \) -Polynomial Identity of Degree Five

  • 会议论文

  • 发表日期：

    2026年

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  • Joseph Tenkodogo,
  • Souleymane Savadogo,
  • Paul Beremwidougou,
  • André Conseibo

摘要

In this paper we study the structure of a class of baric algebras satisfying the identity \( x^{2}x^{3}= (1-\alpha )\omega (x)^{2}x^{3}+ \alpha \omega (x)^{3}x^{2}\) where \(\alpha \in [0;1]\) . Using the Peirce decomposition we establish the links between this class of algebras and other classes such as Bernstein algebras, power-associative algebras, Jordan algebras, principal train algebras and evolution algebras.