5 citations · 18 across the 16 of their papers we have counts for
16 papers
Homological properties and finiteness of reducing invariants
Tokuji Araya, Naoya Hiramatsu, Ryo Takahashi
We study reducing invariants of modules related to certain homological properties. For modules of finite reducing projective dimension, we establish grade inequalities. We prove th…
Vanishing of DHKK complexities for singularity categories and generation of syzygy modules
Tokuji Araya, Kei-ichiro Iima, Ryo Takahashi
Let R be a commutative noetherian ring. In this paper, we study, for the singularity category of R, the vanishing of the complexity in the sense of Dimitrov, Haiden, Kat…
On modules with finite reducing Gorenstein dimension
Tokuji Araya, Olgur Celikbas, Jesse Cook +1
If is a nonzero finitely generated module over a commutative Noetherian local ring such that has finite injective dimension and finite Gorenstein dimension, then it fol…
On reducing homological dimensions over noetherian rings
Tokuji Araya, Ryo Takahashi
Let be a left and right noetherian ring. First, for , we give equivalent conditions for a given -module to be -torsionfree and have -to…
Reducing invariants and total reflexivity
Tokuji Araya, Olgur Celikbas
Motivated by a recent result of Yoshino, and the work of Bergh on reducible complexity, we introduce reducing versions of invariants of finitely generated modules over commutative…
Generation in singularity categories of hypersurfaces of countable representation type
Tokuji Araya, Kei-ichiro Iima, Maiko Ono +1
The Orlov spectrum and Rouquier dimension are invariants of a triangulated category to measure how big the category is, and they have been studied actively. In this paper, we inves…