학술논문

On a generalization of Ulrich modules and its applications
Document Type
Working Paper
Source
Subject
Mathematics - Commutative Algebra
13C13, 13C14, 13D07
Language
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.
Comment: 22 pages