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arXiv · 2412.05261

Localization of unique factorization semidomains

Victor Gonzalez·Harold Polo·Pedro Rodriguez
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Abstract

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.

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Victor Gonzalez, Harold Polo, Pedro Rodriguez. 2024-12-06. Localization of unique factorization semidomains. https://arxiv.org/abs/2412.05261

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