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pro vyhledávání: '"Lyubimtsev, Oleg"'
Autor:
Lyubimtsev, Oleg, Tuganbaev, Askar
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 centrally essential rings, centrally essential quaternion algebras, and gr
Externí odkaz:
http://arxiv.org/abs/2401.12510
Autor:
Lyubimtsev, Oleg, Tuganbaev, Askar
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 any minimal right ideal is contained in the center $C(R)$. A right Ar
Externí odkaz:
http://arxiv.org/abs/2306.06445
Autor:
Lyubimtsev, Oleg, Tuganbaev, Askar
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 $G_S$ of the semigroup $S$ exists and the group algebra $FG_S$ of $G_S$ is centrally essential. The
Externí odkaz:
http://arxiv.org/abs/2204.10518
Autor:
Lyubimtsev, Oleg, Tuganbaev, Askar
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, i.e., maximal right ideals of the ring $R$ are not necessarily ideals.
Externí odkaz:
http://arxiv.org/abs/2204.10507
Autor:
Lyubimtsev, Oleg, Tuganbaev, Askar
A semiring is said to be centrally essential if for every non-zero element $x$, there exist two non-zero central elements $y, z$ with $xy = z$. We give some examples of non-commutative centrally essential semirings and describe some properties of add
Externí odkaz:
http://arxiv.org/abs/2204.10503
Autor:
Lyubimtsev, Oleg, Tuganbaev, Askar
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-free Abelian groups of finite rank with centrally essential endomorph
Externí odkaz:
http://arxiv.org/abs/2008.12261
Autor:
Lyubimtsev, Oleg, Tuganbaev, Askar
We study Abelian groups $A$ with centrally essential endomorphism ring $\text{End}\,A$. If $A$ is a such group which is either a torsion group or a non-reduced group, then the ring $\text{End}\,A$ is commutative. We give examples of Abelian torsion-f
Externí odkaz:
http://arxiv.org/abs/1910.01222
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Autor:
Lyubimtsev, Oleg, Tuganbaev, Askar
Publikováno v:
Communications in Algebra; 2024, Vol. 52 Issue 4, p1614-1621, 8p
Autor:
Lyubimtsev, Oleg, Tuganbaev, Askar
Publikováno v:
Communications in Algebra; 2023, Vol. 51 Issue 6, p2321-2325, 5p