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arXiv · 2404.17680

Characteristic modules over a local ring

Mohsen Gheibi·Ryo Takahashi
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Abstract

Let $R$ be a commutative noetherian local ring, and let $M$ be a finitely generated $R$-module. Inspired by works of Vasconcelos and Briggs on characterization of complete intersection local rings through the homological properties of the conormal module, in this paper, we define the characteristic module T$_M$ and the cocharacteristic module E$_M$ of $M$, and investigate their properties. Our main results include characterizations of Cohen--Macaulay and Gorenstein local rings. Also, we show that if the injective dimension of the conormal module over an almost complete intersection ring is finite, then $R$ is a complete intersection.

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Mohsen Gheibi, Ryo Takahashi. 2024-04-26. Characteristic modules over a local ring. https://arxiv.org/abs/2404.17680

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