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arXiv · 1709.03825

Characterization of Completions of Noncatenary Local Domains and Noncatenary Local UFDs

Chloe I. Avery·Caitlyn Booms·Timothy M. Kostolansky·S. Loepp·Alex Semendinger
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Abstract

We find necessary and sufficient conditions for a complete local ring to be the completion of a noncatenary local (Noetherian) domain, as well as necessary and sufficient conditions for it to be the completion of a noncatenary local (Noetherian) unique factorization domain. We use our first result to demonstrate a large class of quasi-excellent domains that are not excellent, as well as a large class of catenary domains that are not universally catenary. We use our second result to find a larger class of noncatenary local UFDs than was previously known, and we show that there is no bound on how noncatenary a UFD can be.

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Chloe I. Avery, Caitlyn Booms, Timothy M. Kostolansky, S. Loepp, Alex Semendinger. 2017-09-12. Characterization of Completions of Noncatenary Local Domains and Noncatenary Local UFDs. https://arxiv.org/abs/1709.03825

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