O. Bezushchak

collaborators

6 papers

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. BenkoviÄ 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 non…

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…