Abstract:Let $R$ be a commutative noetherian ring, and denote by $\operatorname{mod} R$ the category of finitely generated $R$-modules. In this paper, for an ideal $I$ of $R$, we introduce the full subcategory $\operatorname{mod}_{I}(R)$ of $\operatorname{mod} R$ consisting of modules whose stable annihilators contain $I$, and we investigate its structure. As an application, we explore the syzygy category of maximal Cohen--Macaulay $R$-modules, extending a theorem of Dey and Liu from the Gorenstein case to the Cohen--Macaulay case.
From: Yuki Mifune [view email]
[v1]
Fri, 22 Aug 2025 06:56:24 UTC (15 KB)
[v2]
Wed, 17 Jun 2026 02:52:26 UTC (14 KB)
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