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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, Özg ür Taşdemir
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…
Two Generalizations of Hopfian Abelian Groups
Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith +1
This paper targets to generalize the notion of Hopfian groups in the commutative case by defining the so-called {\bf relatively Hopfian groups} and {\bf weakly Hopfian groups}, and…
On perspective Abelian groups
Grigore Calugareanu, Andrey Chekhlov
As a special case of perspective R-modules, an Abelian goup is called perspective if isomorphic summands have a common complement. In this paper we describe many classes of such gr…