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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…
Generalizations of the Bassian and co-Bassian Properties for Abelian Groups
Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef
Trying to finalize in some way the present subject, this paper targets to generalize substantially the notions of Bassian and co-Bassian groups by introducing the so-called finitel…
Semi-Generalized co-Bassian Groups
Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef
As a common non-trivial generalization of the notion of a generalized co-Bassian group, recently defined by the third author, we introduce the notion of a semi-generalized co-Bassi…
Semi-Generalized Bassian Groups
Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef
As a common non-trivial generalization of the concept of a proper generalized Bassian group, we introduce the notion of a semi-generalized Bassian group and initiate its comprehens…
On Abelian Groups Having Isomorphic Proper Strongly Invariant Subgroups
Andrey R. Chekhlov, Peter V. Danchev
We consider two variants of those Abelian groups with all proper strongly invariant subgroups isomorphic and give an in-depth study of their basic and specific properties in either…