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

Let R be a commutative noetherian local ring and denote by \operatorname{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 \operatorname{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 \operatorname{mod}R in the non-Cohen–Macaulay case.