Vladimir Dotsenko

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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.RA2025

Derived operations satisfy standard identities

Vladimir Dotsenko

A derived operation is a bilinear operation on a commutative associative algebra $A$ defined intrinsically out of its product and several derivations of the product. We show that o…

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…