1 citations · 1 across the 9 of their papers we have counts for
11 papers
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…
Bassian-Finite Abelian Groups
Peter V. Danchev, Patrick W. Keef
We introduce a new class of Abelian groups which lies strictly between the classes of co-Hopfian groups and Dedekind-finite groups, calling these groups {\it Bassian-finite}. We pr…
Hereditarily and Super Generalized co-Bassian Abelian Groups
Peter V. Danchev, Brendan Goldsmith, Patrick W. Keef
We completely characterize by finding necessary and sufficient conditions those co-Bassian and generalized co-Bassian Abelian groups having, respectively, the hereditary or the sup…
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…
On Some Hereditary and Super Classes of Directly Finite Abelian Groups
Peter Danchev, Brendan Goldsmith, Fatemeh Karimi
Continuing recent studies of both the hereditary and super properties of certain classes of Abelian groups, we explore in-depth what is the situation in the quite large class consi…
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…
On Semi-Nil Clean Rings with Applications
M. H. Bien, P. V. Danchev, M. Ramezan-Nassab
We investigate the notion of \textit{semi-nil clean} rings, defined as those rings in which each element can be expressed as a sum of a periodic and a nilpotent element. Among our…
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…
Rings Additively Generated by Periodic Elements
M. H. Bien, P. V. Danchev, M. Ramezan-Nassab
In the present paper, as a generalization of the classical periodic rings, we explore those rings whose elements are additively generated by two (or more) periodic elements by call…