Isomorphism of a Ring
to the Endomorphism Ring of an Abelian Group, Fundamentalnaya i prikladnaya matematika, vol. 9 (2003), no. 1, pp. 231—234.
Annotation
This paper presents necessary and sufficient conditions under which
isomorphism of endomorphism rings of additive groups of arbitrary
associative rings with 1 implies isomorphism of these rings. For a
certain class of abelian groups, we present a criterion which shows
when isomorphism of their endomorphism rings implies isomorphism
of these groups. We demonstrate necessary and sufficient conditions
under which an arbitrary ring is the endomorphism ring of an abelian
group. This solves Problem 84 in [4].
