On a generalization of Ulrich modules and its applications
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.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Tohoku Mathematical Journal
- Volume
- 78
- Issue
- 2
- Publication date
- 1 June 2026
- Language
- EN