Syzygies of Cohen–Macaulay Modules over One Dimensional Cohen–Macaulay Local Rings

Syzygies of Cohen–Macaulay Modules over One Dimensional Cohen–Macaulay Local Rings

We study syzygies of (maximal) Cohen–Macaulay modules over one dimensional Cohen–Macaulay local rings. We assume that rings are generically Gorenstein. We compare these modules to Cohen–Macaulay modules over the endomorphism ring of the maximal ideal. After this comparison, we give several character...

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Veröffentlicht in:Algebras and representation theory 2022-10, Vol.25 (5), p.1061-1070
1. Verfasser: Kobayashi, Toshinori
Format: Artikel
Sprache:eng
Schlagworte:
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Modules
Non-associative Rings and Algebras
Rings (mathematics)
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Zusammenfassung:We study syzygies of (maximal) Cohen–Macaulay modules over one dimensional Cohen–Macaulay local rings. We assume that rings are generically Gorenstein. 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.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-021-10059-5