1 citations · 2 across the 12 of their papers we have counts for
5 papers · 2 filters
On Some Versions of Hopficity for Abelian Groups
Peter V. Danchev, Patrick W. Keef
We completely describe in certain important cases the class of commutative co-finitely Hopfian groups as defined by Bridson-Groves-Hillman- Martin in the journal Groups, Geometry,…
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…
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…
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…