Absolute Ideals of Almost Completely Decomposable Abelian Groups

2023/10/10 by Е. И. Компанцева, Kompantseva, Ekaterina, A. A. Tuganbaev +1 · 1 citation
Mathematics · #16B99 #20K30 #20K99 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2310.07041

openalex publication_date 2023/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the class A₀ of Abelian block-rigid CRQ-groups of ring type. A subgroup A of an Abelian group G is called an \textsfabsolute ideal of the group G if A is an ideal in any ring on G. We describe principal absolute ideals of groups in A₀. This allows to prove that any group in A₀ is an afi-group, i.e., a group G such that any absolute ideal of G is a fully invariant subgroup.

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