Related papers: On modules with self Tor vanishing
In this paper we are concerned with the vanishing of $\textnormal{Tor}$ over complete intersection rings. Building on results of C. Huneke, D. Jorgensen and R. Wiegand, and, more recently, H. Dao, we obtain new results showing that good…
The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated free modules over a noetherian local ring. Then we show that over such a ring,…
A vanishing theorem is proved for Ext groups over non-commutative graded algebras. Along the way, an "infinite" version is proved of the non-commutative Auslander-Buchsbaum theorem.
We make use of the concepts of Tor-rigid and rigid-test modules, among others, to investigate the interplay between cohomology vanishing and the finiteness of several homological dimensions such as projective, injective and Gorenstein…
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 local domains. We utilize Hochster's theta invariant and show…
Let $R$ be a perfect ring and $T$ be an $R$-module. We study characterizations of sincere modules, sincere silting modules and tilting modules in terms of various vanishing conditions. It is proved that $T$ is sincere silting if and only if…
In this paper, we study module theoretic definitions of the Baer and related ring concepts. We say a module is s.Baer if the right annihilator of a nonempty subset of the module is generated by an idempotent in the ring. We show that s.Baer…
Let R be a Cohen-Macaulay ring and M a maximal Cohen-Macaulay R-module. Inspired by recent striking work by Iyama, Burban-Iyama-Keller-Reiten and Van den Bergh we study the question of when the endomorphism ring of M has finite global…
In this paper, we study the problem when a finitely generated torsionless module is projective. Let $\Lambda$ be an Artinian local algebra with radical square zero. Then a finitely generated torsionless $\Lambda$-module $M$ is projective if…
We study H. Dao's invariant $\eta_c^R$ of pairs of modules defined over a complete intersection ring $R$ of codimension $c$ having an isolated singularity. Our main result is that $\eta_c^R$ vanishes for all pairs of modules when $R$ is a…
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 Noetherian local rings. Our main result considers modules…
Let $(R,\mathfrak{m},\mathbb{k})$ be an equicharacteristic one-dimensional complete local domain over an algebraically closed field $\mathbb{k}$ of characteristic 0. R. Berger conjectured that R is regular if and only if the universally…
Let R be an associative ring with identity, and let T be a tilting right R-module, with S=End(T). It is known that if R is a Noetherian algebra that satisfies the Auslander-Reiten conjecture, then so is S. In this paper, we consider the…
For finitely generated modules $M$ and $N$ over a Gorenstein local ring $R$, one has $depth M + depth N= depth(M\otimes N) +depth R$, i.e., the depth formula holds, if $M$ and $N$ are Tor-independent and Tate homology…
The existence of the Gorenstein projective precovers over arbitrary rings is an open question. It is known that if the ring has finite Gorenstein global dimension, then every module has a Gorenstein projective precover. We prove here a…
We study the question if projective modules over formal Laurent series rings are extended. We relate this question to the Bass-Quillen conjecture for commutative regular local rings and to the Hermite ring conjecture for all commutative…
This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in…
We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations, and generalize a theorem of O. Celikbas-Takahashi. Our work produces new classes of rigid and test modules, in particular over local…
In this paper, we compare annihilators of Tor and Ext modules of finitely generated modules over a commutative noetherian ring. For local Cohen--Macaulay rings, one of our results refines a theorem of Dao and Takahashi.
It is proved that if one of the finite modules M and N, over a local ring R, has reducible complexity and has finite Gorenstein dimension then the depth formula holds, provided TorR_i(M,N) = 0 for i>>0. We also study the vanishing of…