5 papers · 1 filter
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…
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…
Generalized Bassian and other Mixed Abelian Groups with Bounded p-Torsion
Peter V. Danchev, Patrick W. Keef
It is known that a mixed abelian group G with torsion T is Bassian if, and only if, it has finite torsion-free rank and has finite p-torsion (i.e., each Tp is finite). It is also k…