Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank

Abstract

We consider the class A 0 of Abelian block-rigid CRQ-groups of ring type. A subgroup A of an Abelian group G is called an absolute ideal of the group G if A is an ideal in any ring on G. We describe principal absolute ideals of groups in A 0 . This allows to prove that any group in A 0 is an af i-group, i.e., a group G such that any absolute ideal of G is a fully invariant subgroup.