3 papers
math.RA2024
On Centrally Essential Rings
Oleg Lyubimtsev, Askar Tuganbaev
A ring with center is said to be centrally essential if the module is an essential extension of the module . In this paper, we study properties of ideals of cent…
math.RA2023
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…
math.RA2022
Centrally Essential Semigroup Algebras
Oleg Lyubimtsev, Askar Tuganbaev
For a cancellative semigroup S and a field F, it is proved that the semigroup algebra FS is centrally essential if and only if the group of fractions of the semigroup exi…