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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.07096 |
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| _version_ | 1866914866851217408 |
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| author | Rizzo, Pedro del Valle, Joel Torres Torres-Gomez, Alexander |
| author_facet | Rizzo, Pedro del Valle, Joel Torres Torres-Gomez, Alexander |
| contents | In the realm of supercommutative superrings, this article investigates the unique factorization of elements. We build upon recent findings by Naser et. al. concerning similar results in noncommutative symmetric rings with zerodivisors, delving deeper into the ramifications. Strikingly, we demonstrate that any unique factorization superdomain necessarily takes the form of a superfield, further characterizing them as Artinian superrings with Krull superdimension 0 | d. Furthermore, we discover that a straightforward analogue of the well-known Auslander-Buchsbaum Theorem does not hold true in the supercommutative setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on Unique Factorization in Superrings Rizzo, Pedro del Valle, Joel Torres Torres-Gomez, Alexander Rings and Algebras In the realm of supercommutative superrings, this article investigates the unique factorization of elements. We build upon recent findings by Naser et. al. concerning similar results in noncommutative symmetric rings with zerodivisors, delving deeper into the ramifications. Strikingly, we demonstrate that any unique factorization superdomain necessarily takes the form of a superfield, further characterizing them as Artinian superrings with Krull superdimension 0 | d. Furthermore, we discover that a straightforward analogue of the well-known Auslander-Buchsbaum Theorem does not hold true in the supercommutative setting. |
| title | A Note on Unique Factorization in Superrings |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2402.07096 |