When does an infinite ring have a finite compressed commuting graph?
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916478097293312 |
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| author | Boroja, Ivan-Vanja Bukovšek, Damjana Kokol Stopar, Nik |
| author_facet | Boroja, Ivan-Vanja Bukovšek, Damjana Kokol Stopar, Nik |
| contents | We show that any infinite ring has an infinite nonunital compressed commuting graph. We classify all infinite unital rings with finite unital compressed commuting graph, using semidirect product of rings as our main tool. As a consequence we also classify infinite unital rings with only finitely many unital subrings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07358 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | When does an infinite ring have a finite compressed commuting graph? Boroja, Ivan-Vanja Bukovšek, Damjana Kokol Stopar, Nik Rings and Algebras 05C25, 16B99, 16S70 We show that any infinite ring has an infinite nonunital compressed commuting graph. We classify all infinite unital rings with finite unital compressed commuting graph, using semidirect product of rings as our main tool. As a consequence we also classify infinite unital rings with only finitely many unital subrings. |
| title | When does an infinite ring have a finite compressed commuting graph? |
| topic | Rings and Algebras 05C25, 16B99, 16S70 |
| url | https://arxiv.org/abs/2411.07358 |