5 citations · 11 across the 24 of their papers we have counts for
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Rings whose ideals are close to automorphism-invariant
Adel Abyzov, Truong Cong Quynh, Askar Tuganbaev
We consider rings whose one-sided ideals are close to automorphism-invariant modules. We study rings in which every (finitely generated) right ideal is automorphism invariant and r…
On Realization and Isomorphism Problems for Formal Matrix Rings
Piotr Krylov, Askar Tuganbaev
We consider realization and isomorphism problems for formal matrix rings over a given ring. Principal multiplier matrices of such rings play an important role in this case.\\ The w…
Centrally Essential Rings and Semirings
Askar Tuganbaev
This work is a review of results about centrally essential rings and semirings. A ring (resp., semiring) is said to be centrally essential if it is either commutative or satisfy th…
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…
Ideals and Factor Rings of Centrally Essential Rings
Oleg Lyubimtsev, Askar Tuganbaev
It is proved that the ring with center , such that the module is an essential extension of the module , is not necessarily right quasi-invariant,…
Centrally Essential Semirings
Oleg Lyubimtsev, Askar Tuganbaev
A semiring is said to be centrally essential if for every non-zero element , there exist two non-zero central elements with . We give some examples of non-commuta…