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math.AC2019
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…
math.AC2019
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…
math.AC2019
Powers of the maximal ideal and vanishing of (co)homology
Olgur Celikbas, Ryo Takahashi
We prove that each positive power of the maximal ideal of a commutative Noetherian local ring is Tor-rigid, and strongly-rigid. This gives new characterizations of regularity and,…