Syzygies of Cohen-Macaulay modules over one dimensional Cohen-Macaulay local rings

Abstract

We study syzygies of (maximal) Cohen-Macaulay modules over one dimensional Cohen-Macaulay local rings. We compare these modules to Cohen-Macaulay modules over the endomorphism ring of the maximal ideal. After this comparison, we give several characterizations of almost Gorenstein rings in terms of syzygies of Cohen-Macaulay modules.

9 pages. Remark 3.3. was added

References in corpus (1)

• Rejective subcategories of artin algebras and orders

Cited by in corpus (4)

• Ulrich modules over Cohen-Macaulay local rings with minimal multiplicity
• Reflexive modules over Arf local rings
• On reflexive and $I$-Ulrich modules over curve singularities
• Canonical Degrees of Cohen-Macaulay Rings and Modules: a Survey