Generalizations of the Bassian and co-Bassian Properties for Abelian Groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910364790161408 |
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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 |