FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 8, PAGES 109-138

Torsion Abelian RAI-groups

Pham Thi Thu Thuy

Abstract

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A subgroup $A$ of an Abelian group $G$ is called its absolute ideal if $A$ is an ideal of any ring on $G$. An Abelian group is called an RAI-group if there exists a ring on it in which every ideal is absolute. The problem of describing RAI-groups was formulated by L. Fuchs (Problem 93). In this paper, absolute ideals of torsion Abelian groups and torsion Abelian RAI-groups are described.

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Last modified: March 23, 2013