Syzygies of Cohen-Macaulay modules over one dimensional Cohen-Macaulay local rings
Toshinori Kobayashi
TL;DR
This paper investigates the syzygies of Cohen-Macaulay modules over one-dimensional Cohen-Macaulay local rings, comparing them to modules over endomorphism rings, and characterizes almost Gorenstein rings through these syzygies.
Contribution
It introduces new characterizations of almost Gorenstein rings based on syzygies of Cohen-Macaulay modules, expanding understanding of their structure.
Findings
Characterizations of almost Gorenstein rings via syzygies
Comparison between Cohen-Macaulay modules over different rings
Insights into the structure of Cohen-Macaulay modules
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Advanced Topics in Algebra