A generalization of the dimension and radius of a subcategory of modules and its applications

2024/01/20 by Mifune, Yuki · 2 citations
#13C60 #13D07 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2401.11153

Abstract

Let R be a commutative noetherian local ring and denote by mod R the category of finitely generated R-modules. In this paper, we give some evaluations of the singular locus of R and annihilators of Tor and Ext from a viewpoint of the finiteness of dimensions/radii of full subcategories of mod R. As an application, we recover a theorem of Dey and Takahashi when R is Cohen--Macaulay. Moreover, we obtain the divergence of the dimensions of specific full subcategories of mod R in non-Cohen--Macaulay case.

Cited by

• Structure of modules stably annihilated by a fixed ideal
• On local rings of finite syzygy representation type

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