𝐿-dimension for modules over a local ring

Pub Date : 2021-01-01 DOI:10.1090/conm/773/15534

Courtney R. Gibbons, David A. Jorgensen, J. Striuli

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Abstract

We introduce a new homological dimension for finitely generated modules over a commutative local ring R R , which is based on a complex derived from a free resolution L L of the residue field of R R , and called L L -dimension. We prove several properties of L L -dimension, give some applications, and compare L L -dimension to complete intersection dimension.

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𝐿-dimension用于本地环上的模块

在交换局部环R R上，我们引入了一个新的有限生成模的同调维数，该同调维数是基于R R的剩余域的自由分辨率L L派生的复维数，称为L L维数。证明了L - L维数的几个性质，给出了一些应用，并将L - L维数与完全交维数进行了比较。

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