Varieties of bicommutative algebras with identity of degree three

Vesselin Drensky; Bekzat Zhakhayev

Varieties of bicommutative algebras with identity of degree three

Rings and Algebras 2026-05-12 v1

Authors: Vesselin Drensky , Bekzat Zhakhayev

Abstract

The variety of bicommutative algebras is the class of all nonassociative algebras satisfying the polynomial identities $(x_1x_2)x_3=(x_1x_3)x_2$ and $x_1(x_2x_3)=x_2(x_1x_3)$ . In this paper we provide a complete description of varieties of bicommutative algebras over a field of characteristic zero that satisfy a polynomial identity of degree three. Furthermore, we establish a sufficient and necessary condition for a variety of bicommutative algebras to have a distributive lattice of subvarieties.

Keywords

bicommutative algebras nonassociative algebras polynomial identity degree three identity subvariety lattice characteristic zero

Cite

@article{arxiv.2605.09512,
  title  = {Varieties of bicommutative algebras with identity of degree three},
  author = {Vesselin Drensky and Bekzat Zhakhayev},
  journal= {arXiv preprint arXiv:2605.09512},
  year   = {2026}
}

Varieties of bicommutative algebras with identity of degree three

Abstract

Keywords

Cite

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