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 …
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 …
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 …
Powers of the maximal ideal and vanishing of (co) homology
O Celikbas, R Takahashi - Glasgow Mathematical Journal, 2021 - cambridge.org
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, in …
ring is Tor-rigid and strongly rigid. This gives new characterizations of regularity and, in …
On the second rigidity theorem of Huneke and Wiegand
O Celikbas, R Takahashi - Proceedings of the American Mathematical …, 2019 - ams.org
In 2007 Huneke and Wiegand announced in an erratum that one of the conclusions of their
depth formula theorem is flawed due to an incorrect convention for the depth of the zero …
depth formula theorem is flawed due to an incorrect convention for the depth of the zero …
Homological dimensions, the Gorenstein property, and special cases of some conjectures
Our purpose in this work is multifold. First, we provide general criteria for the finiteness of the
projective and injective dimensions of a finite module $ M $ over a (commutative) …
projective and injective dimensions of a finite module $ M $ over a (commutative) …
Some aspects of local cohomology theory
RF Holanda - 2022 - repositorio.ufpb.br
This work is about some features of local cohomology theory. We develop a new tool called
Mayer-Vietoris spectral sequence that allows us to study several local cohomology modules …
Mayer-Vietoris spectral sequence that allows us to study several local cohomology modules …
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 …
Quasi-injective dimension
M Gheibi - Journal of Pure and Applied Algebra, 2024 - Elsevier
Following our previous work about quasi-projective dimension [11], in this paper, we
introduce quasi-injective dimension as a generalization of injective dimension. We recover …
introduce quasi-injective dimension as a generalization of injective dimension. We recover …