Abstract

Abstract Let 𝐺 be an abelian group. A subgroup of 𝐺 is called an absolute ideal of 𝐺 if it is an ideal in any ring on 𝐺. In this paper, we describe the principal absolute ideals of groups in the class A 0 \mathcal{A}_{0} , which consists of reduced abelian block-rigid CRQ-groups of ring type. This allows us to prove that every absolute ideal of a group 𝐺 from A 0 \mathcal{A}_{0} is a fully invariant subgroup of 𝐺.

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