Geodesic
Isomorphism of a ring to the endomorphism ring of an Abelian group
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 231-234 
V. M. Misyakov. Isomorphism of a ring to the endomorphism ring of an Abelian group. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 231-234. http://geodesic.mathdoc.fr/item/FPM_2003_9_1_a12/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.”

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