Maximal Cohen–Macaulay tensor products and vanishing of Ext modules
In this paper, we investigate the maximal Cohen–Macaulay property of tensor products of
modules, and then give criteria for projectivity of modules in terms of vanishing of Ext …
modules, and then give criteria for projectivity of modules in terms of vanishing of Ext …
Some characterizations of local rings via reducing dimensions
In this paper we study homological dimensions of finitely generated modules over
commutative Noetherian local rings, called reducing homological dimensions. We obtain …
commutative Noetherian local rings, called reducing homological dimensions. We obtain …
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 …
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 …
Auslander–Reiten conjecture and finite injective dimension of Hom
D Ghosh, R Takahashi - Kyoto Journal of Mathematics, 2024 - projecteuclid.org
For a finitely generated module M over a commutative Noetherian ring R, we settle the
Auslander–Reiten conjecture when at least one of Hom R (M, R) and Hom R (M, M) has …
Auslander–Reiten conjecture when at least one of Hom R (M, R) and Hom R (M, M) has …
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 …
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 …
Two generalizations of Auslander–Reiten duality and applications
A Sadeghi, R Takahashi - 2019 - projecteuclid.org
Two generalizations of Auslander-Reiten duality and applications Page 1 Two generalizations of
Auslander–Reiten duality and applications Arash Sadeghi and Ryo Takahashi …
Auslander–Reiten duality and applications Arash Sadeghi and Ryo Takahashi …
Bass and Betti numbers of a module and its deficiency modules
T Fiel, R Holanda - Journal of Commutative Algebra, 2024 - projecteuclid.org
This paper aims to provide several relations between Bass and Betti numbers of a given
module and its deficiency modules. Such relations and the tools used throughout allow us to …
module and its deficiency modules. Such relations and the tools used throughout allow us to …
[PDF][PDF] Reflexivity revisited
M Asgharzadeh - arXiv preprint arXiv:1812.00830, 2018 - arxiv.org
arXiv:1812.00830v6 [math.AC] 14 Dec 2022 Page 1 arXiv:1812.00830v6 [math.AC] 14 Dec
2022 REFLEXIVITY REVISITED MOHSEN ASGHARZADEH Abstract. We study some aspects of …
2022 REFLEXIVITY REVISITED MOHSEN ASGHARZADEH Abstract. We study some aspects of …