A. A. Tuganbaev

most citedAbsolute Ideals of Almost Completely Decomposable Abelian Groups

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math.RA2024

Multiplicative Automorphisms of Incidence Algebras

Evgenii Kaigorodov, Piotr Krylov, Askar Tuganbaev

Let $I (X, R)$ be the incidence algebra of the preordered set $X$ over the ring $R$ . In the case of a finite connected partially ordered set $X$ , we prove that the subgroup of inner…

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

On Rings over Which All Modules Are Direct Sums of Distributive Modules

Askar Tuganbaev

A module is said to be \textsf{distributive} if the lattice of its submodules is distributive. A direct sum of distributive modules is called a \textsf{semidistributive} module. In…

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.RA2023

Incidence Rings: Automorphisms and Derivations

Piotr Krylov, Askar Tuganbaev

We study automorphisms, isomorphisms, and derivations of the incidence algebra $I (X, R)$ , where $X$ is preordered set and $R$ is an algebra over some commutative ring $T$ .

math.RA2023

Formal Matrix Rings: Isomorphism Problem

Piotr Krylov, Askar Tuganbaev

We consider the isomorphism problem for formal matrix rings over a given ring. Principal factor matrices of such rings play an important role in this case. The work is supported by…