MATHEMATICS

Torsion abelian $afi$-groups

Pham Thi Thu Thuy

Moscow State Pedagogical University

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 $afi$-group if every its absolute ideal is a fully invariant subgroup. In this paper descriptions of afi-groups in the class of fully-transitive torsion groups (particularly, separable torsion groups) and divisible torsion groups are given.

Keywords: abelian group, ring on a group, absolute ideal, fully invariant subgroup, $afi$-group.

UDC: 512.541

Received: 13.05.2011