5 citations · 11 across the 24 of their papers we have counts for
32 papers
Extensions of Centrally Essential Rings
Oleg Lyubimtsev, Askar Tuganbaev
A non-zero unital ring is said to be centrally essential if for every nonzero element of , there exist non-zero central elements and with . In the paper,…
On Centrally Essential Subrings of Formal Triangular Matrix Rings
Oleg Lyubimtsev, Askar Tuganbaev
A ring with a non-zero identity element is said to be centrally essential if for any non-zero element , there exist non-zero central elements such that $ax =…
Absolute Ideals of Almost Completely Decomposable Abelian Groups
Ekaterina Kompantseva, Askar Tuganbaev
We consider the class of Abelian block-rigid -groups of ring type. A subgroup of an Abelian group is called an \textsf{absolute ideal} of the group …
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…
Centrally Essential Factor Rings and Subdirect Indecomposability
Oleg Lyubimtsev, Askar Tuganbaev
Let be a ring and let , be its Jacobson radical and center, correspondingly. If is a centrally essential ring and the factor ring is commutative, then…
Incidence Rings: Automorphisms and Derivations
Piotr Krylov, Askar Tuganbaev
We study automorphisms, isomorphisms, and derivations of the incidence algebra , where is preordered set and is an algebra over some commutative ring .