On the finiteness of radii of resolving subcategories
Commutative Algebra
2023-08-11 v1 Representation Theory
Abstract
Let R be a commutative noetherian ring. Denote by mod R the category of finitely generated R-modules. In this paper, we investigate the finiteness of the radii of resolving subcategories of mod R with respect to a fixed semidualizing module. As an application, we give a partial positive answer to a conjecture of Dao and Takahashi: we prove that for a Cohen-Macaulay local ring R, a resolving subcategory of mod R has infinite radius whenever it contains a canonical module and a non-MCM module of finite injective dimension.
Keywords
Cite
@article{arxiv.2308.05296,
title = {On the finiteness of radii of resolving subcategories},
author = {Yuki Mifune},
journal= {arXiv preprint arXiv:2308.05296},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1111.2902 by other authors