O. Bezushchak

activity

20202026

most citedAutomorphisms and derivations of affine commutative and PI-algebras

1 citations · 1 across the 7 of their papers we have counts for

collaborators

10 papers

math.RA2026

Lie Algebras of Locally Finite Derivations over Fields of Positive Characteristic

Oksana Bezushchak, Anatoliy Petravchuk

Let $F$ be a field of positive characteristic, and let $A$ be a finitely generated commutative associative $F$ -algebra. We study Lie subalgebras of $D er A$ generated by locally…

math.RA2026

Lie and Jordan Isomorphisms of Algebras of Triangular Matrices over Associative Rings

Oksana Bezushchak

We describe Lie and Jordan isomorphisms of algebras of triangular matrices over associative rings.

math.RA2026

When Is a Bogolyubov Automorphism Inner?

Nikita Arskyi, Oksana Bezushchak

Let $V$ be an infinite-dimensional vector space over a field of characteristic not equal to $2$ . Given a nondegenerate quadratic form $f$ on $V$ , we consider the Clifford algebra $…

math.RA2026

Normalized Rank- and Determinant-Preserving Mappings of Locally Matrix Algebras

Oksana Bezushchak

Let $A$ be a unital locally matrix algebra. Among the examples of such algebras are: (1) an infinite tensor product $\otimes M_{n_{i}} (F)$ of matrix algebras over a field $\…

math.RA2025

Jordan homomorphisms of triangular algebras over noncommutative algebras

Oksana Bezushchak

D. Benkovič described Jordan homomorphisms of algebras of triangular matrices over a commutative unital ring without additive $2$ -torsion. We extend this result to the case of nonc…

math.RA2025

Derivations of Lie Algebras of Vector Fields in Infinitely Many Variables

Oksana Bezushchak, Iryna Kashuba

Let $W_{X} (F)$ be the Lie algebra of all derivations of the polynomial algebra $F [X]$ in infinitely many variables. We describe all derivations of $W_{X} (F)$ …

math.RA2025

On Lie isomorphisms of rings

Oksana Bezushchak, Iryna Kashuba, Efim Zelmanov

An associative ring $A$ gives rise to the Lie ring $A^{(-)} = (A, [a, b] = ab - ba)$ . The subject of isomorphisms of Lie rings $A^{(-)}$ and $[A, A]$ has attracted considerable attention i…

math.RA2022★ 1 cited

Automorphisms and derivations of affine commutative and PI-algebras

Oksana Bezushchak, Anatoliy Petravchuk, Efim Zelmanov

We prove analogs of A.~Selberg's result for finitely generated subgroups of $Aut (A)$ and of Engel's theorem for subalgebras of $Der (A)$ for a finitely generated assoc…

math.RA2020

Spectra of locally matrix algebras

Oksana Bezushchak

We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix a…

math.RA2020

On the Lie structure of locally matrix algebras

Oksana Bezushchak

Let $A$ be a unital locally matrix algebra over a field $F$ of characteristic different from $2.$ We find necessary and sufficient condition for the Lie algebra $A\diagup\…