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math.AC2023
Two theorems on the vanishing of Ext
Olgur Celikbas, Souvik Dey, Toshinori Kobayashi +2
We prove two theorems on the vanishing of Ext over commutative Noetherian local rings. Our first theorem shows that there are no Burch ideals which are rigid over non-regular local…
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
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…