5 citations · 18 across the 16 of their papers we have counts for
14 papers · 1 filter
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…
On the vanishing of self extensions over Cohen-Macaulay local rings
Tokuji Araya, Olgur Celikbas, Arash Sadeghi +1
The celebrated Auslander-Reiten Conjecture, on the vanishing of self extensions of a module, is one of the long-standing conjectures in ring theory. Although it is still open, ther…
Remarks on torsionfreeness and its applications
Tokuji Araya, Kei-ichiro Iima
In this article, we shall characterize torsionfreeness of modules with respect to a semidualizing module in terms of the Serre's condition (S_n). As its applications, we give a cha…
A Homological dimension related to AB rings
Tokuji Araya
There are many homological dimensions which are closely related to ring theoretic properties. The notion of a AB ring has been introduced by Huneke and Jorgensen. It has nice homol…
On the left perpendicular category of the modules of finite projective dimension
Tokuji Araya, Kei-ichiro Iima, Ryo Takahashi
In this paper, we characterize several properties of commutative notherian local rings in terms of the left perpendicular category of the category of finitely generated modules of…
On the structure of Cohen-Macaulay modules over hypersurfaces of countable Cohen-Macaulay representation type
Tokuji Araya, Kei-ichiro Iima, Ryo Takahashi
Let R be a complete local hypersurface over an algebraically closed field of characteristic different from two, and suppose that R has countable Cohen-Macaulay representation type.…
A generalization of a theorem of Foxby
Tokuji Araya, Ryo Takahashi
In this paper, it is proved that a commutative noetherian local ring admitting a finitely generated module of finite projective and injective dimensions with respect to a semiduali…
The Auslander-Reiten conjecture for Gorenstein rings
Tokuji Araya
The Nakayama conjecture is one of the most important conjectures in ring theory. The Auslander-Reiten conjecture is closely related to it. The purpose of this note is to show that…
Homological invariants associated to semi-dualizing bimodules
Tokuji Araya, Ryo Takahashi, Yuji Yoshino
Cohen-Macaulay dimension for modules over a commutative noetherian local ring has been defined by A. A. Gerko. That is a homological invariant sharing many properties with projecti…