18 citations · 19 across the 6 of their papers we have counts for
6 papers
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 : every subalgebra of every free algebra in this variety is itself fr…
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 and . In t…
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…
Free bicommutative superalgebras
Vesselin Drensky, Nurlan Ismailov, Manat Mustafa +1
We introduce the variety of bicommutative superalgebras over an arbitrary field of characteristic different from 2. The variety consists of all nonas…
Free assosymmetric algebras as modules of groups
Askar S. Dzhumadil'daev, Bekzat K. Zhakhayev
An algebra with identities is called {\it assosymmetric}, where is associator. We study -module, -module and -module…
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…