Generalizations of the Bassian and co-Bassian Properties for Abelian Groups

Fuente: arXiv
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Autori principali: Chekhlov, Andrey R., Danchev, Peter V., Keef, Patrick W.
Natura: Preprint
Pubblicazione: 2024
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author Chekhlov, Andrey R.
Danchev, Peter V.
Keef, Patrick W.
author_facet Chekhlov, Andrey R.
Danchev, Peter V.
Keef, Patrick W.
contents Trying to finalize in some way the present subject, this paper targets to generalize substantially the notions of Bassian and co-Bassian groups by introducing the so-called finitely (co-)Bassian groups, semi (co-)Bassian groups, fully generalized (co-)Bassian groups, absolutely generalized (co-)Bassian groups and establishing their crucial properties and characterizations. In fact, some of the concepts give nothing new by coinciding in the reduced case with the well-known (co-)Bassian property. However, in some of the definitions, the situation is slightly more complicated and we obtain a few new and interesting things by showing that the extensions of the Bassian and co-Bassian properties are totally distinct each other.
format Preprint
id arxiv_https___arxiv_org_abs_2403_08096
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Generalizations of the Bassian and co-Bassian Properties for Abelian Groups
Chekhlov, Andrey R.
Danchev, Peter V.
Keef, Patrick W.
Group Theory
Rings and Algebras
20K21
Trying to finalize in some way the present subject, this paper targets to generalize substantially the notions of Bassian and co-Bassian groups by introducing the so-called finitely (co-)Bassian groups, semi (co-)Bassian groups, fully generalized (co-)Bassian groups, absolutely generalized (co-)Bassian groups and establishing their crucial properties and characterizations. In fact, some of the concepts give nothing new by coinciding in the reduced case with the well-known (co-)Bassian property. However, in some of the definitions, the situation is slightly more complicated and we obtain a few new and interesting things by showing that the extensions of the Bassian and co-Bassian properties are totally distinct each other.
title Generalizations of the Bassian and co-Bassian Properties for Abelian Groups
topic Group Theory
Rings and Algebras
20K21
url https://arxiv.org/abs/2403.08096