Two theorems on the vanishing of Ext
O Celikbas, T Kobayashi, H Matsui… - arXiv preprint arXiv …, 2023 - arxiv.org
We prove two theorems on the vanishing of Ext over commutative Noetherian local rings.
Our first theorem shows that, over non-regular Cohen-Macaulay local domains, there are no …
Our first theorem shows that, over non-regular Cohen-Macaulay local domains, there are no …
An Ext-Tor duality theorem, cohomological dimension, and applications
R Holanda, CB Miranda-Neto - arXiv preprint arXiv:2312.09725, 2023 - arxiv.org
We provide a duality theorem between Ext and Tor modules over a Cohen-Macaulay local
ring possessing a canonical module, and use it to prove some freeness criteria for finite …
ring possessing a canonical module, and use it to prove some freeness criteria for finite …
Vanishing of (co) homology, freeness criteria, and the Auslander-Reiten conjecture for Cohen-Macaulay Burch rings
R Holanda, CB Miranda-Neto - arXiv preprint arXiv:2212.05521, 2022 - arxiv.org
We establish new results on (co) homology vanishing and Ext-Tor dualities, and derive a
number of freeness criteria for finite modules over Cohen-Macaulay local rings. In the main …
number of freeness criteria for finite modules over Cohen-Macaulay local rings. In the main …
On the ideal case of a conjecture of Huneke and Wiegand
O Celikbas, S Goto, R Takahashi… - Proceedings of the …, 2019 - cambridge.org
A conjecture of Huneke and Wiegand claims that, over one-dimensional commutative
Noetherian local domains, the tensor product of a finitely generated, non-free, torsion-free …
Noetherian local domains, the tensor product of a finitely generated, non-free, torsion-free …
On the Auslander–Reiten conjecture for Cohen–Macaulay local rings
S Goto, R Takahashi - Proceedings of the American Mathematical Society, 2017 - ams.org
This paper studies vanishing of Ext modules over Cohen–Macaulay local rings. The main
result of this paper implies that the Auslander–Reiten conjecture holds for maximal Cohen …
result of this paper implies that the Auslander–Reiten conjecture holds for maximal Cohen …
The Auslander-Reiten conjecture for certain non-Gorenstein Cohen-Macaulay rings
S Kumashiro - Journal of Pure and Applied Algebra, 2023 - Elsevier
Abstract The Auslander-Reiten conjecture is a notorious open problem about the vanishing
of Ext modules. In a Cohen-Macaulay complete local ring R with a parameter ideal Q, the …
of Ext modules. In a Cohen-Macaulay complete local ring R with a parameter ideal Q, the …
Criteria for prescribed bound on projective dimension
VH Jorge-Pérez, CB Miranda-Neto - Communications in Algebra, 2021 - Taylor & Francis
We establish a prescribed upper bound for the projective dimension of a finitely generated
module over a Cohen-Macaulay local ring (with canonical module) satisfying certain …
module over a Cohen-Macaulay local ring (with canonical module) satisfying certain …
Tensor products and solutions to two homological conjectures for Ulrich modules
C Miranda-Neto, T Souza - Proceedings of the American Mathematical …, 2024 - ams.org
We address the problem of when the tensor product of two finitely generated modules over a
Cohen-Macaulay local ring is Ulrich in the generalized sense of Goto et al., and in particular …
Cohen-Macaulay local ring is Ulrich in the generalized sense of Goto et al., and in particular …
Auslander--Reiten conjecture for normal rings
K Kimura - arXiv preprint arXiv:2304.03956, 2023 - arxiv.org
In this paper, sufficient conditions for finitely generated modules over a commutative
noetherian ring to be projective are given in terms of vanishing of Ext modules. One of the …
noetherian ring to be projective are given in terms of vanishing of Ext modules. One of the …
Self-injective commutative rings have no nontrivial rigid ideals
H Lindo - arXiv preprint arXiv:1710.01793, 2017 - arxiv.org
arXiv:1710.01793v2 [math.AC] 13 Oct 2017 Page 1 arXiv:1710.01793v2 [math.AC] 13 Oct
2017 SELF-INJECTIVE COMMUTATIVE RINGS HAVE NO NONTRIVIAL RIGID IDEALS …
2017 SELF-INJECTIVE COMMUTATIVE RINGS HAVE NO NONTRIVIAL RIGID IDEALS …