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We consider the class $\mathcal{A}_0$ of Abelian block-rigid $CRQ$-groups ofring type. A subgroup $A$ of an Abelian group $G$ is called an \textsf{absoluteideal} of the group $G$ if $A$ is an ideal in any ring on $G$. We describeprincipal absolute ideals of groups in $\mathcal{A}_0$. This allows to provethat any group in $\mathcal{A}_0$ is an $afi$-group, i.e., a group $G$ suchthat any absolute ideal of $G$ is a fully invariant subgroup.

Absolute Ideals of Almost Completely Decomposable Abelian Groups