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 …
Homological dimensions of Burch ideals, submodules and quotients
D Ghosh, A Saha - Journal of Pure and Applied Algebra, 2024 - Elsevier
The notion of Burch ideals and Burch submodules were introduced (and studied) by Dao-
Kobayashi-Takahashi in 2020 and Dey-Kobayashi in 2022 respectively. The aim of this …
Kobayashi-Takahashi in 2020 and Dey-Kobayashi in 2022 respectively. The aim of this …
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 …
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 …
On the vanishing of (co) homology for modules admitting certain filtrations
O Celikbas, Y Yao - arXiv preprint arXiv:2304.07641, 2023 - arxiv.org
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 …
certain filtrations, and generalize a theorem of O. Celikbas-Takahashi. Our work produces …
[PDF][PDF] Freeness criteria via vanishing of $ Tor$
M Asgharzadeh, E Mahdavi - arXiv preprint arXiv:2204.02871, 2022 - arxiv.org
arXiv:2204.02871v2 [math.AC] 26 May 2022 Page 1 arXiv:2204.02871v2 [math.AC] 26 May
2022 FREENESS CRITERIA VIA VANISHING OF Tor MOHSEN ASGHARZADEH AND ELHAM …
2022 FREENESS CRITERIA VIA VANISHING OF Tor MOHSEN ASGHARZADEH AND ELHAM …
Some Categorical Aspects of Commutative Algebra
S Dey - 2023 - search.proquest.com
The purpose of this work is to study commutative Noetherian rings by studying certain
subcategories of the category of finitely generated modules over such rings. We begin by …
subcategories of the category of finitely generated modules over such rings. We begin by …