22 citations · 57 across the 23 of their papers we have counts for
28 papers
On the test properties of the Frobenius endomorphism
Olgur Celikbas, Arash Sadeghi, Yongwei Yao
In this paper, we prove two theorems concerning the test properties of the Frobenius endomorphism over commutative Noetherian local rings of prime characteristic . Our first the…
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…
Remarks on a conjecture of Huneke and Wiegand and the vanishing of (co)homology
Olgur Celikbas, Uyen Le, Hiroki Matsui +1
In this paper we study a long-standing conjecture of Huneke and Wiegand which is concerned with the torsion submodule of certain tensor products of modules over one-dimensional loc…
A study of the cohomological rigidity property
Mohsen Asgharzadeh, Olgur Celikbas, Arash Sadeghi
In this paper, motivated by a work of Luk and Yau, and Huneke and Wiegand, we study various aspects of the cohomological rigidity property of tensor product of modules over commuta…
On an example concerning the second rigidity theorem
Olgur Celikbas, Hiroki Matsui, Arash Sadeghi
In this paper we revisit an example of Celikbas and Takahashi concerning the reflexivity of tensor products of modules. We study Tor-rigidity and the Hochster--Huneke graph with ve…
A study of Tate homology via the approximation theory with applications to the depth formula
Olgur Celikbas, Li Liang, Arash Sadeghi +1
In this paper we are concerned with absolute, relative and Tate Tor modules. In the first part of the paper we generalize a result of Avramov and Martsinkovsky by using the Ausland…
Linkage of modules by reflexive morphisms
Fatemeh Dehghani-Zadeh, Mohammad-T. Dibaei, Arash Sadeghi
In this paper, we introduce and study the notion of linkage of modules by reflexive homomorphisms. This notion unifies and generalizes several known concepts of linkage of modules…
On modules with reducible complexity
Olgur Celikbas, Arash Sadeghi, Naoki Taniguchi
In this paper we generalize a result, concerning a depth equality over local rings, proved independently by Araya and Yoshino, and Iyengar. Our result exploits complexity, a concep…
Two generalizations of Auslander-Reiten duality and applications
Arash Sadeghi, Ryo Takahashi
This paper extends Auslander-Reiten duality in two directions. As an application, we obtain various criteria for freeness of modules over local rings in terms of vanishing of Ext m…
Notes on linkage of modules
Arash Sadeghi
Let R be a Cohen-Macaulay local ring. It is shown that under some mild conditions, the Cohen-Macaulayness property is preserved under linkage. We also study the connection of (S_n)…
Maximal Cohen-Macaulay tensor products
Olgur Celikbas, Arash Sadeghi
In this paper we are concerned with the following question: if the tensor product of finitely generated modules and over a local complete intersection domain is maximal Coh…
Resolving subcategories closed under certain operations and a conjecture of Dao and Takahashi
Arash Sadeghi, Ryo Takahashi
Let R be a commutative Noetherian local ring with residue field k. Let X be a resolving subcategory of finitely generated R-modules. This paper mainly studies when X contains k or…
Tensoring with the Frobenius endomorphism
Olgur Celikbas, Arash Sadeghi, Yongwei Yao
Let be a commutative Noetherian Cohen-Macaulay local ring that has positive dimension and prime characteristic. Li proved that the tensor product of a finitely generated non-fr…
Linkage of modules with respect to a semidualizing module
Mohammad-T. Dibaei, Arash Sadeghi
The notion of linkage with respect to a semidualizing module is introduced. It is shown that over a Cohen-Macaulay local ring with canonical module, every Cohen-Macaulay module of…
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…
On the depth of tensor products of modules
Arash Sadeghi
The depth of tensor product of modules over a Gorenstein local ring is studied. For finitely generated modules M and N over a Gorenstein local ring R, under some assumptions on the…
On the ideal case of a conjecture of Auslander and Reiten
Olgur Celikbas, Kei-ichiro Iima, Arash Sadeghi +1
A celebrated conjecture of Auslander and Reiten claims that a finitely generated module that has no extensions with over an Artin algebra must be projective. Th…
Vanishing of relative homology and depth of tensor products
Olgur Celikbas, Li Liang, Arash Sadeghi
For finitely generated modules and over a Gorenstein local ring , one has , i.e., the depth formula holds, if and …
Symmetry in vanishing of Tate cohomology over Gorenstein rings
Arash Sadeghi
We investigate symmetry in the vanishing of Tate cohomology for finitely generated modules over local Gorenstein rings. For finitely generated R-modules M and N over Gorenstein loc…
Associated Primes and Syzygies of Linked Modules
Olgur Celikbas, Mohammad T. Dibaei, Mohsen Gheibi +2
Motivated by the notion of geometrically linked ideals, we show that over a Gorenstein local ring , if a Cohen-Macaulay -module of grade is linked to an -module $N…
Linkage of finite G_C-dimension modules
Arash Sadeghi
Let R be a semiperfect commutative Noetherian ring and C a semidualizing R-module. We study the theory of linkage for modules of finite G_C-dimension. For a horizontally linked R-m…
Linkage of modules and the Serre conditions
Mohammad T. Dibaei, Arash Sadeghi
Let be semiperfect commutative Noetherian ring and be a semidualizing --module. The connection of the Serre condition on a horizontally linked -module of fini…
Homological dimensions of rigid modules
Olgur Celikbas, Mohsen Gheibi, Majid Rahro Zargar +1
We obtain various characterizations of commutative Noetherian local rings $(R, \fm)$ in terms of homological dimensions of certain finitely generated modules. For example, we estab…
Bounds on depth of tensor products of modules
Olgur Celikbas, Arash Sadeghi, Ryo Takahashi
Let be a local complete intersection ring and let and be nonzero finitely generated -modules. We employ Auslander's transpose in the study of the vanishing of Tor an…