4 papers
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 Torsion-Free Rings of Finite Rank
Oleg Lyubimtsev, Askar Tuganbaev
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…
Local Centrally Essential Subalgebras of Triangular Algebras
O. V. Lyubimtsev, A. A. Tuganbaev
We study local centrally essential subalgebras in the algebra of all upper triangular matrices over a field of characteristic . It is proved that the algebras of upper trian…
Centrally Essential Endomorphism Rings of Abelian Groups
Oleg Lyubimtsev, Askar Tuganbaev
We study Abelian groups with centrally essential endomorphism ring . If is a such group which is either a torsion group or a non-reduced group, then the ring…