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Absolute ideals of almost completely decomposable abelian groups

  • Ekaterina Kompantseva und Askar Tuganbaev EMAIL logo
Veröffentlicht/Copyright: 2. Oktober 2024

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 , 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 is a fully invariant subgroup of 𝐺.

Acknowledgements

The authors are grateful to the reviewers for very helpful comments.

  1. Communicated by: Evgenii I. Khukhro

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Received: 2023-12-03
Revised: 2024-09-04
Published Online: 2024-10-02
Published in Print: 2025-03-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 17.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jgth-2023-0281/html
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