83 citations · 480 across the 45 of their papers we have counts for
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math.AC2014
Maximal Cohen-Macaulay approximations and Serre's condition
Hiroki Matsui, Ryo Takahashi
This paper studies the relationship between Serre's condition and Auslander--Buchweitz's maximal Cohen--Macaulay approximations. It is proved that a Gorenstein local ring…
math.AC2014★ 7 cited
Singularity categories and singular equivalences for resolving subcategories
Hiroki Matsui, Ryo Takahashi
Let $\X$ be a resolving subcategory of an abelian category. In this paper we investigate the singularity category $\ds(\underline\X)=\db(\mod\underline\X)/\kb(\proj(\mod\underline\…
math.AC2014
Prethick subcateogries of modules and characterizations of local rings
Hiroki Matsui, Hayato Murata
This paper studies characterizing local rings in terms of homological dimensions. The key tool is the notion of a prethick subcategory which we introduce in this paper. Our methods…