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arXiv · 2605.09512

Varieties of bicommutative algebras with identity of degree three

Vesselin Drensky·Bekzat Zhakhayev
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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.

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Vesselin Drensky, Bekzat Zhakhayev. 2026-05-10. Varieties of bicommutative algebras with identity of degree three. https://arxiv.org/abs/2605.09512

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