Absolute ideals of almost completely decomposable abelian groups

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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi mathvariant="script">A</m:mi> <m:mn>0</m:mn> </m:msub> </m:math> A₀ , 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi mathvariant="script">A</m:mi> <m:mn>0</m:mn> </m:msub> </m:math> A₀ is a fully invariant subgroup of 𝐺.