6 citations · 33 across the 20 of their papers we have counts for
21 papers · 1 filter
Depth formula for modules of finite reducing projective dimension
Olgur Celikbas, Toshinori Kobayashi, Brian Laverty +1
We prove that the depth formula holds for two finitely generated Tor-independent modules over Cohen-Macaulay local rings if one of the modules considered has finite reducing projec…
Two theorems on the vanishing of Ext
Olgur Celikbas, Souvik Dey, Toshinori Kobayashi +2
We prove two theorems on the vanishing of Ext over commutative Noetherian local rings. Our first theorem shows that there are no Burch ideals which are rigid over non-regular local…
Semidualizing Modules over Numerical Semigroup Rings
Ela Celikbas, Hugh Geller, Toshinori Kobayashi
A semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen-Macaulay ring , the ring itself and its canonical module are always realized as…
On the projective dimension of tensor products of modules
Olgur Celikbas, Souvik Dey, Toshinori Kobayashi
In this paper, we consider finitely generated modules over commutative Noetherian rings whose tensor products have finite projective dimension. We construct examples of modules of…
Some characterizations of local rings via reducing dimensions
Olgur Celikbas, Souvik Dey, Toshinori Kobayashi +1
In this paper we study homological dimensions of finitely generated modules over commutative Noetherian local rings, called reducing homological dimensions. We obtain new character…
On the reducing projective dimension of the residue field
Olgur Celikbas, Souvik Dey, Toshinori Kobayashi +1
In this paper we are concerned with certain invariants of modules, called reducing invariants, which have been recently introduced and studied by Araya-Celikbas and Araya-Takahashi…
The set of trace ideals of curve singularities
Toshinori Kobayashi, Shinya Kumashiro
This paper mainly focuses on commutative local domains of dimension one. We then obtain a criterion for a ring to have a finite number of trace ideals in terms of integrally closed…
Vanishing of (co)homology of Burch and related submodules
Souvik Dey, Toshinori Kobayashi
We introduce the notion of Burch submodules and weakly -full submodules of modules over local rings and study their properties. One of our main results shows that Burc…
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 a class of Burch ideals and a conjecture of Huneke and Wiegand
Olgur Celikbas, Toshinori Kobayashi
In this paper we are concerned with a long-standing conjecture of Huneke and Wiegand. We introduce a new class of ideals and prove thateach ideal from such class satisfies the conc…
Trace of canonical modules, annihilator of Ext, and classes of rings close to being Gorenstein
Hailong Dao, Toshinori Kobayashi, Ryo Takahashi
In this note we study trace ideals of canonical modules. Characterizations of the trace ideals in terms of annihilators of certain Ext modules are given. We apply our results to st…
The Huneke-Wiegand conjecture and middle terms of almost split sequences
Toshinori Kobayashi
Let R be a Gorenstein local domain of dimension one. We show that a nonfree maximal Cohen--Macaulay R-module M possessing more than one nonfree indecomposable summand in the middle…
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…
Maximal Cohen-Macaulay modules that are not locally free on the punctured spectrum
Toshinori Kobayashi, Justin Lyle, Ryo Takahashi
We say that a Cohen-Macaulay local ring has finite -representation type if there exist only finitely many isomorphism classes of indecomposable maxima…
Local rings with self-dual maximal ideal
Toshinori Kobayashi
Let R be a Cohen-Macaulay local ring possessing a canonical module. In this paper we consider when the maximal ideal of R is self-dual, i.e. it is isomorphic to its canonical dual…
Rings whose ideals are isomorphic to trace ideals
Toshinori Kobayashi, Ryo Takahashi
Let R be a commutative noetherian ring. Lindo and Pande have recently posed the question asking when every ideal of R is isomorphic to some trace ideal of R. This paper studies thi…
Ulrich modules over Cohen-Macaulay local rings with minimal multiplicity
Toshinori Kobayashi, Ryo Takahashi
Let R be a Cohen-Macaulay local ring. In this paper we study the structure of Ulrich -modules mainly in the case where R has minimal multiplicity. We explore generation of Ulric…
Syzygies of Cohen-Macaulay modules over one dimensional Cohen-Macaulay local rings
Toshinori Kobayashi
We study syzygies of (maximal) Cohen-Macaulay modules over one dimensional Cohen-Macaulay local rings. We compare these modules to Cohen-Macaulay modules over the endomorphism ring…
On delta invariants and indices of ideals
Toshinori Kobayashi
Let R be a Cohen-Macaulay local ring with a canonical module. We consider Auslander's (higher) delta invariants of powers of certain ideals of R. Firstly, we shall provide some con…
On a question of Buchweitz about ranks of syzygies of modules of finite length
Toshinori Kobayashi
Let R be a local ring of dimension d. Buchweitz asks if the rank of the d-th syzygy of a module of finite lengh is greater than or equal to the rank of the d-th syzygy of the resid…
Syzygies of Cohen-Macaulay modules and Grothendieck groups
Toshinori Kobayashi
We study the converse of a theorem of Butler and Auslander-Reiten. We show that a Cohen-Macaulay local ring with an isolated singularity has only finitely many isomorphism classes…