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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.05261 |
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| _version_ | 1866910731415322624 |
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| author | Gonzalez, Victor Polo, Harold Rodriguez, Pedro |
| author_facet | Gonzalez, Victor Polo, Harold Rodriguez, Pedro |
| contents | A semidomain is a subsemiring of an integral domain. Within this class, a unique factorization semidomain (UFS) is characterized by the property that every nonzero, nonunit element can be factored into a product of finitely many prime elements. In this paper, we investigate the localization of semidomains, focusing specifically on UFSs. We demonstrate that the localization of a UFS remains a UFS, leading to the conclusion that a UFS is either a unique factorization domain or is additively reduced. In addition, we provide an example of a subsemiring $\mathfrak{S}$ of $\mathbb{R}$ such that $(\mathfrak{S}, \cdot)$ and $(\mathfrak{S}, +)$ are both half-factorial, shedding light on a conjecture posed by Baeth, Chapman, and Gotti. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Localization of unique factorization semidomains Gonzalez, Victor Polo, Harold Rodriguez, Pedro Commutative Algebra A semidomain is a subsemiring of an integral domain. Within this class, a unique factorization semidomain (UFS) is characterized by the property that every nonzero, nonunit element can be factored into a product of finitely many prime elements. In this paper, we investigate the localization of semidomains, focusing specifically on UFSs. We demonstrate that the localization of a UFS remains a UFS, leading to the conclusion that a UFS is either a unique factorization domain or is additively reduced. In addition, we provide an example of a subsemiring $\mathfrak{S}$ of $\mathbb{R}$ such that $(\mathfrak{S}, \cdot)$ and $(\mathfrak{S}, +)$ are both half-factorial, shedding light on a conjecture posed by Baeth, Chapman, and Gotti. |
| title | Localization of unique factorization semidomains |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2412.05261 |