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arXiv · 2308.06606

On a generalization of Ulrich modules and its applications

Ela Celikbas·Olgur Celikbas·Justin Lyle·Ryo Takahashi·Yongwei Yao
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Abstract

We study a modified version of the classical Ulrich modules, which we call $c$-Ulrich. Unlike the traditional setting, $c$-Ulrich modules always exist. We prove that these modules retain many of the essential properties and applications observed in the literature. Additionally, we reveal their significance as obstructions to Cohen-Macaulay properties of tensor products. Leveraging this insight, we show the utility of these modules in testing the finiteness of homological dimensions across various scenarios.

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Ela Celikbas, Olgur Celikbas, Justin Lyle, Ryo Takahashi, Yongwei Yao. 2023-08-12. On a generalization of Ulrich modules and its applications. https://arxiv.org/abs/2308.06606

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