This article is cited in 16 papers

Torsion-free rings

E. I. Kompantseva

Moscow State Pedagogical University

Abstract: The aim of this paper is to study the correlation between the properties of rings and the structure of their additive groups. In this paper, all multiplications on reduced algebraically compact groups and on divisible torsion-free Abelian groups are described. Absolute Jacobson radicals and absolute nil-radicals in some classes of Abelian groups are found. Using these results, we will give a description of semisimple groups and also of groups on which every ring is a nilpotent ring (a nil-ring, a radical ring) in some concerned classes of Abelian groups.

UDC: 512.541

 English version: Journal of Mathematical Sciences (New York), 2010, 171:2, 213–247

Bibliographic databases:

• 
•