Local rings with quasi-decomposable maximal ideal
S Nasseh, R Takahashi - Mathematical Proceedings of the …, 2020 - cambridge.org
Let (R, 𝔪) be a commutative noetherian local ring. In this paper, we prove that if 𝔪 is
decomposable, then for any finitely generated R-module M of infinite projective dimension 𝔪 …
decomposable, then for any finitely generated R-module M of infinite projective dimension 𝔪 …
[HTML][HTML] Applications and homological properties of local rings with decomposable maximal ideals
We construct a local Cohen–Macaulay ring R with a prime ideal p∈ Spec (R) such that R
satisfies the uniform Auslander condition (UAC), but the localization R p does not satisfy …
satisfies the uniform Auslander condition (UAC), but the localization R p does not satisfy …
Extremal growth of Betti numbers and trivial vanishing of (co) homology
J Lyle, J Montaño - Transactions of the American Mathematical Society, 2020 - ams.org
A Cohen–Macaulay local ring $ R $ satisfies trivial vanishing if $\operatorname {Tor} _i^ R
(M, N)= 0$ for all large $ i $ implies that $ M $ or $ N $ has finite projective dimension. If $ R …
(M, N)= 0$ for all large $ i $ implies that $ M $ or $ N $ has finite projective dimension. If $ R …
Almost Gorenstein rings arising from fiber products
N Endo, S Goto, R Isobe - Canadian Mathematical Bulletin, 2021 - cambridge.org
The purpose of this paper is, as part of the stratification of Cohen–Macaulay rings, to
investigate the question of when the fiber products are almost Gorenstein rings. We show …
investigate the question of when the fiber products are almost Gorenstein rings. We show …
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 …
Minimal free resolutions of fiber products
H Geller - Proceedings of the American Mathematical Society, 2022 - ams.org
We consider a local (or standard graded) ring $ R $ with ideals $\mathcal {I}'$, $\mathcal {I}
$, $\mathcal {J}'$, and $\mathcal {J} $ satisfying certain Tor-vanishing constraints. We …
$, $\mathcal {J}'$, and $\mathcal {J} $ satisfying certain Tor-vanishing constraints. We …
Gluing of analytic space germs, invariants and Watanabe's conjecture
TH de Freitas, VHJ Pérez, AJ Miranda - Israel Journal of Mathematics, 2021 - Springer
This paper deals with the subject of singularities of a germ of an analytic space given by the
gluing of germs of complex analytic spaces and some invariants such as degree of a finite …
gluing of germs of complex analytic spaces and some invariants such as degree of a finite …
Homological invariants of powers of fiber products
HD Nguyen, T Vu - Acta Mathematica Vietnamica, 2019 - Springer
Let R and S be polynomial rings of positive dimensions over a field k. Let I⊆ R, J⊆ S be non-
zero homogeneous ideals none of which contains a linear form. Denote by F the fiber …
zero homogeneous ideals none of which contains a linear form. Denote by F the fiber …
On Betti numbers of the gluing of germs of formal complex spaces
TH Freitas, VHJ Pérez… - Mathematische …, 2023 - Wiley Online Library
In this paper, we show that the gluing of germs of formal complex spaces is also a formal
complex space. Moreover, we study the Betti numbers of the gluing of formal complex …
complex space. Moreover, we study the Betti numbers of the gluing of formal complex …
Finite homological dimension of Hom and vanishing of Ext
For finitely generated modules $ M $ and $ N $ over a commutative Noetherian local ring $
R $, we give various sufficient criteria for detecting freeness of $ M $ or $ N $ via vanishing …
R $, we give various sufficient criteria for detecting freeness of $ M $ or $ N $ via vanishing …