Structure of modules stably annihilated by a fixed ideal

2025/08/22 by Mifune, Yuki
#13C14 #13C60 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.16137

Abstract

Let R be a commutative noetherian ring, and denote by mod R the category of finitely generated R-modules. In this paper, for an ideal I of R, we introduce the full subcategory mod_I(R) of 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.

Citations

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• Syzygy modules with semidualizing or G-projective summands
• Stable module theory

Related

• On the annihilators and attached primes of top local cohomology modules
• Annihilators of local cohomology modules via a classification theorem of the dominant resolving subcategories
• A generalization of the dimension and radius of a subcategory of modules and its applications
• I-Cohen Macaulay modules
• On Annihilator Multiplication Modules