The goal of this paper is to give a survey of how endomorphism rings can be used to study
the behavior of modules. While the first part considers modules over arbitrary rings, the …

Groups and modules with isomorphic endomorphism rings are known, in certain cases, to
be necessarily isomorphic. When such a ring isomorphism is replaced by an anti …

With an abelian group A one associates the ring End A End\nolimits A of its endomorphisms.
This is an associative ring with 1 which frequently reflects several relevant features of the …

This paper contains a review of results on endomorphism rings of Abelian groups. On one
hand, this rapidly developing section of contemporary algebra can be considered as a part …

Every Abelian group can be related to an associative ring with an identity element, the ring
of all its endomorphisms. Recently the theory of endomor phism rings of Abelian groups has …

Models, Modules and Abelian Groups, 121–133 O de Gruyter 2008 Page 132 Models,
Modules and Abelian Groups, 121–133 O de Gruyter 2008 Endomorphisms and …

Corner's Theorem started the modern approach to endomorphism rings of torsion-free
abelian groups. From this point of view many results are collected stating realizability …

This note is based on three papers by ALS Corner, H. Zassenhaus and MCR Butler,
respectively ([4, 8, 3]). Corner showed in his celebrated paper [4] that any countable ring R …

We are going to prove two theorems on endomorphism rings of rank one abelian groups
with simply presented torsion. In Theorem 1, we describe when the endomorphism rings of …

The review presents an analysis of results of the Abelian group theory, as well as rings and
modules, which concern the definability of algebraic structures by their endomorphism rings …