5 papers
Rings with Clean-Like Properties: Endomorphism, Matrix and Structural Theorems
Adel N. Abyzov, Andrey R. Chekhlov, Peter V. Danchev +1
We investigate three clean-like properties for arbitrary rings, for endomorphism rings of abelian groups and for matrix rings over finite fields. Specifically, we study and establi…
Strongly and Uniformly Strongly co-Hopfian Abelian Groups
Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef
We consider the so-called {\it strongly co-Hopfian} and {\it uniformly strongly co-Hopfian} Abelian groups, significantly generalizing some important results due to Abdelalim in th…
On Two Generalizations of Perspective Abelian Groups
Andrey R. Chekhlov, Peter V. Danchev, Ãzg ür TaÅdemir
We are generalizing in two non-trivial ways the recently defined perspective Abelian groups to the so-called IC-groups and TP-groups, respectively, and obtain numerous results in t…
Completely Inert Subgroups of Abelian Groups
Andrey R. Chekhlov, Peter V. Danchev
We define and study in-depth the so-called completely inert and uniformly completely inert subgroups of Abelian groups. We curiously show that a subgroup is completely inert exactl…
Two Generalizations of co-Hopfian Abelian Groups
Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef
By defining the classes of generalized co-Hopfian and relatively co-Hopfian groups, respectively, we consider two expanded versions of the generalized co-Bassian groups and of the…