7 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, 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…
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…