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math.AC2021★ 8 cited
Auslander-Reiten conjecture and finite injective dimension of Hom
Dipankar Ghosh, Ryo Takahashi
For a finitely generated module over a commutative Noetherian ring , we settle the Auslander-Reiten conjecture when at least one of and ${\rm Hom}_R(M,M…
math.AC2021★ 1 cited
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…
math.AC2021
On the Subcategories of n-Torsionfree Modules and Related Modules
Souvik Dey, Ryo Takahashi
Let R be a commutative noetherian ring. Denote by mod R the category of finitely generated R-modules. In this paper, we study n-torsionfree modules in the sense of Auslander and Br…