60 citations · 392 across the 111 of their papers we have counts for
10 papers · 1 filter
Filtrations in module categories, derived categories and prime spectra
Hiroki Matsui, Ryo Takahashi
Let R be a commutative noetherian ring. The notion of n-wide subcategories of Mod R is introduced and studied in Matsui-Nam-Takahashi-Tri-Yen in relation to the cohomological dimen…
Quasi-projective dimension
Mohsen Gheibi, David A. Jorgensen, Ryo Takahashi
In this paper, we introduce a new homological invariant called quasi-projective dimension, which is a generalization of projective dimension. We discuss various properties of quasi…
Cohomological dimensions of specialization-closed subsets and subcategories of modules
Hiroki Matsui, Tran Tuan Nam, Ryo Takahashi +2
Let R be a commutative noetherian ring. In this paper, we study specialization-closed subsets of Spec R. More precisely, we first characterize the specialization-closed subsets in…
On the radius of the category of extensions of matrix factorizations
Kaori Shimada, Ryo Takahashi
Let be a commutative noetherian ring. The extensions of matrix factorizations of non-zerodivisors of form a full subcategory of finitely generated modules o…
Burch ideals and Burch rings
Hailong Dao, Toshinori Kobayashi, Ryo Takahashi
We introduce the notion of Burch ideals and Burch rings. They are easy to define, and can be viewed as generalization of many well-known concepts, for example integrally closed ide…
A topology on the set of isomorphism classes of maximal Cohen--Macaulay modules
Naoya Hiramatsu, Ryo Takahashi
In this paper, we introduce a topology on the set of isomorphism classes of finitely generated modules over an associative algebra. Then we focus on the relative topology on the se…