14 papers · 1 filter
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…
An extension of a depth inequality of Auslander
Olgur Celikbas, Uyen Le, Hiroki Matsui
In this paper, we consider a depth inequality of Auslander which holds for finitely generated Tor-rigid modules over commutative Noetherian local rings. We raise the question of wh…
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 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…
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…
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…