Abstract:
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.
Fulltext:
PDF file (293 kB)