Vanishing of (co) homology of Burch and related submodules
S Dey, T Kobayashi - Illinois Journal of Mathematics, 2023 - projecteuclid.org
We introduce the notion of Burch submodules and weakly m-full submodules of modules
over a local ring (R, m) and study their properties. One of our main results shows that Burch …
over a local ring (R, m) and study their properties. One of our main results shows that Burch …
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 …
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 …
On a class of Burch ideals and a conjecture of Huneke and Wiegand
O Celikbas, T Kobayashi - Collectanea mathematica, 2022 - Springer
In this paper we are concerned with a long-standing conjecture of Huneke and Wiegand. We
introduce a new class of ideals and prove that each ideal from such class satisfies the …
introduce a new class of ideals and prove that each ideal from such class satisfies the …
On one-dimensional local rings and Berger's conjecture
CB Miranda-Neto - Proceedings of the Edinburgh Mathematical …, 2023 - cambridge.org
ON ONE-DIMENSIONAL LOCAL RINGS AND BERGER’S CONJECTURE Page 1 Proceedings
of the Edinburgh Mathematical Society (2023) 66, 437–452 doi:10.1017/S0013091523000214 …
of the Edinburgh Mathematical Society (2023) 66, 437–452 doi:10.1017/S0013091523000214 …
On a generalization of Ulrich modules and its applications
E Celikbas, O Celikbas, J Lyle, R Takahashi… - arXiv preprint arXiv …, 2023 - arxiv.org
We study a modified version of the classical Ulrich modules, which we call $ c $-Ulrich.
Unlike the traditional setting, $ c $-Ulrich modules always exist. We prove that these …
Unlike the traditional setting, $ c $-Ulrich modules always exist. We prove that these …
Auslander-Reiten and Huneke-Wiegand conjectures over quasi-fiber product rings
TH Freitas, VH PÉrez, R Wiegand… - arXiv preprint arXiv …, 2022 - arxiv.org
In this paper we explore consequences of the vanishing of ${\rm Ext} $ for finitely generated
modules over a quasi-fiber product ring $ R $; that is, $ R $ is a local ring such that …
modules over a quasi-fiber product ring $ R $; that is, $ R $ is a local ring such that …
Some applications of a lemma by Hanes and Huneke
C Miranda-Neto - Proceedings of the American Mathematical Society, 2024 - ams.org
Our main goal in this note is to use a version of a lemma by Hanes and Huneke to provide
characterizations of when certain one-dimensional reduced local rings are regular. This is of …
characterizations of when certain one-dimensional reduced local rings are regular. This is of …
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 …