FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 5, PAGES 93-101

Rings on almost completely decomposable Abelian groups

E. I. Kompantseva

Abstract

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The absolute radical of an Abelian group $G$ is the intersection of radicals of all associative rings with additive group $G$. L. Fuchs formulated the problem on a description of absolute radicals of Abelian groups. For a group from some class of almost completely decomposable Abelian groups the absolute Jacobson radical is described. In the class of almost completely decomposable Abelian groups semisimple groups are described.

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