FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 1, PAGES 231-234

**Isomorphism of a ring to the endomorphism ring of an Abelian
group**

V.
M.
Misyakov

Abstract

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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 L. Fuchs' "Infinite Abelian Groups."

Location: http://mech.math.msu.su/~fpm/eng/k03/k031/k03113h.htm

Last modified: April 4, 2004.