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Non-existence of Ulrich modules over Cohen-Macaulay local rings
- Publication Year :
- 2024
-
Abstract
- Over a Cohen-Macaulay local ring, the minimal number of generators of a maximal Cohen-Macaulay module is bounded above by its multiplicity. In 1984 Ulrich asked whether there always exist modules for which equality holds; such modules are known nowadays as Ulrich modules. We answer this question in the negative by constructing families of two dimensional Cohen-Macaulay local rings that have no Ulrich modules. Some of these examples are Gorenstein normal domains; others are even complete intersection domains, though not normal.<br />Comment: 12 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2403.15566
- Document Type :
- Working Paper