Overrings of half-factorial orders Article Swipe

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Jason G. Boynton , Jim Coykendall , Grant Moles , Charles T. Morrow ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2504.11394

The behavior of factorization properties in various ring extensions is a central theme in commutative algebra. Classically, the UFDs are (completely) integrally closed and tend to behave well in standard ring extensions, with the notable exception of power series extension. The half-factorial property is not as robust; HFDs need not be integrally closed and the half-factorial property is not necessarily preserved in integral extensions or even localizations. Here we exhibit classes of HFDs that behave well in (almost) integral extensions, resolve an open question on the behavior of the boundary map, and give a squeeze theorem for elasticity in certain domains.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2504.11394
PDF: https://arxiv.org/pdf/2504.11394
OA Status: green
OpenAlex ID: https://openalex.org/W4416052790

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DOI: https://doi.org/10.48550/arxiv.2504.11394

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Title: Overrings of half-factorial orders

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-04-15

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Authors: Jason G. Boynton, Jim Coykendall, Grant Moles, Charles T. Morrow

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Landing page: https://arxiv.org/abs/2504.11394

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PDF URL: https://arxiv.org/pdf/2504.11394

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Cited by: 0

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