O. Lyubimtsev

activity

20192024

collaborators

6 papers

math.RA2024

On Centrally Essential Rings

Oleg Lyubimtsev, Askar Tuganbaev

A ring $R$ with center $C$ is said to be centrally essential if the module $R_{C}$ is an essential extension of the module $C_{C}$ . In this paper, we study properties of ideals of cent…

math.RA2023

Centrally Essential Factor Rings and Subdirect Indecomposability

Oleg Lyubimtsev, Askar Tuganbaev

Let $R$ be a ring and let $J (R)$ , $C (R)$ be its Jacobson radical and center, correspondingly. If $R$ is a centrally essential ring and the factor ring $R / J (R)$ is commutative, then…

math.RA2022

Ideals and Factor Rings of Centrally Essential Rings

Oleg Lyubimtsev, Askar Tuganbaev

It is proved that the ring $R$ with center $Z (R)$ , such that the module $R_{Z (R)}$ is an essential extension of the module $Z (R)_{Z (R)}$ , is not necessarily right quasi-invariant,…

math.RA2020

Centrally Essential Torsion-Free Rings of Finite Rank

Oleg Lyubimtsev, Askar Tuganbaev

It is proved that centrally essential rings, whose additive groups of finite rank are torsion-free groups of finite rank, are quasi-invariant but not necessarily invariant. Torsion…

math.RA2020

Local Centrally Essential Subalgebras of Triangular Algebras

O. V. Lyubimtsev, A. A. Tuganbaev

We study local centrally essential subalgebras in the algebra of all upper triangular matrices over a field of characteristic $\neq = 2$ . It is proved that the algebras of upper trian…

math.RA2019

Centrally Essential Endomorphism Rings of Abelian Groups

Oleg Lyubimtsev, Askar Tuganbaev

We study Abelian groups $A$ with centrally essential endomorphism ring $End A$ . If $A$ is a such group which is either a torsion group or a non-reduced group, then the ring…