Bekzat Zhakhayev

activity

20172026

most citedNoetherianity and Specht problem for varieties of bicommutative algebras

18 citations · 18 across the 3 of their papers we have counts for

collaborators

5 papers

math.RA2026

A Nielsen--Schreier variety of algebras without the PBW property

Vladimir Dotsenko, Bekzat Zhakhayev

We prove the Nielsen--Schreier property for the variety of algebras defined by the identity $x (x^{2})^{2} = (x^{2})^{2} x$ : every subalgebra of every free algebra in this variety is itself fr…

math.RA2026

Varieties of bicommutative algebras with identity of degree three

Vesselin Drensky, Bekzat Zhakhayev

The variety of bicommutative algebras is the class of all nonassociative algebras satisfying the polynomial identities $(x_{1} x_{2}) x_{3} = (x_{1} x_{3}) x_{2}$ and $x_{1} (x_{2} x_{3}) = x_{2} (x_{1} x_{3})$ . In t…

math.RA2024

Distributive lattices of varieties of Novikov algebras

Vladimir Dotsenko, Bekzat Zhakhayev

We prove that a variety of Novikov algebras has a distributive lattice of subvarieties if and only if the lattice of its subvarieties defined by identities of degree three is distr…

math.RA2018

Free assosymmetric algebras as modules of groups

Askar S. Dzhumadil'daev, Bekzat K. Zhakhayev

An algebra with identities $(a, b, c) = (a, c, b) = (b, a, c)$ is called {\it assosymmetric}, where $(x, y, z) = (x y) z - x (y z)$ is associator. We study $S_{n}$ -module, $A_{n}$ -module and $G L_{n}$ -module…

math.RA2017★ 18 cited

Noetherianity and Specht problem for varieties of bicommutative algebras

Vesselin Drensky, Bekzat K. Zhakhayev

Nonassociative algebras satisfying the polynomial identities x(yz)=y(xz) and (xy)z=(xz)y are called bicommutative. We prove the following results: (i) Finitely generated bicommutat…