1 citations · 1 across the 10 of their papers we have counts for
10 papers
On strongly G-regular rings
Kaito Kimura, Yuki Mifune, Yuya Otake +1
A noetherian ring is called G-regular when all finitely generated Gorenstein projective modules are projective. In this paper, we study rings satisfying the stronger condition that…
On local rings of finite syzygy representation type
Souvik Dey, Kaito Kimura, Jian Liu +1
Let be a commutative Noetherian local ring. We characterize when its completion has an isolated singularity, thereby strengthening the Dao-Takahashi refinement of the Auslander…
An approach to Martsinkovsky's invariant via Auslander's approximation theory
Yuya Otake
Auslander developed a theory of the -invariant for finitely generated modules over commutative Gorenstein local rings, and Martsinkovsky extended this theory to the -invarian…
Generation of singularity categories and infinite injective dimension locus via annihilation of cohomologies
Souvik Dey, Jian Liu, Yuki Mifune +1
Let R be a commutative Noetherian ring. We establish a close relationship between the strong generation of the singularity category of R and the nonvanishing of the annihilator of…
On the Auslander-Bridger-Yoshino theory for complexes of finitely generated projective modules
Yuya Otake
Let R be a two-sided noetherian ring. Auslander and Bridger developed a theory of projective stabilization of the category of finitely generated R-modules, which is called the stab…
On the vanishing of Ext modules over a local unique factorization domain with an isolated singularity
Kaito Kimura, Justin Lyle, Yuya Otake +1
This paper provides a method to get a noetherian equicharacteristic local UFD with an isolated singularity from a given noetherian complete equicharacteristic local ring, preservin…
Ext modules related to syzygies of the residue field
Yuya Otake
Let R be a commutative noetherian ring. In this paper, we find out close relationships between the module M being embedded in a module of projective dimension at most n and the (n+…
Stable categories of spherical modules and torsionfree modules
Yuya Otake
Auslander and Bridger introduced the notions of n-spherical modules and n-torsionfree modules. In this paper, we construct an equivalence between the stable category of n-spherical…
Morphisms represented by monomorphisms with n-torsionfree cokernel
Yuya Otake
We introduce and study a new class of morphisms which includes morphisms represented by monomorphisms in the sense of Auslander and Bridger. As an application, we give not only an…
Maximal Cohen-Macaulay tensor products and vanishing of Ext modules
Kaito Kimura, Yuya Otake, Ryo Takahashi
In this paper, we investigate the maximal Cohen-Macaulay property of tensor products of modules, and then give criteria for projectivity of modules in terms of vanishing of Ext mod…