Results 1 to 10 of about 87 (85)

The Weak (Gorenstein) Global Dimension of Coherent Rings with Finite Small Finitistic Projective Dimension

Journal of Mathematics
The small finitistic dimension of a ring is determined as the supremum projective dimensions among modules with finite projective resolutions. This paper seeks to establish that, for a coherent ring R with a finite weak (resp.
Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou   +3 more
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Finitistic dimension conjectures via Gorenstein projective dimension [PDF]

Journal of Algebra, 2022
It is a well-known result of Auslander and Reiten that contravariant finiteness of the class $\mathcal{P}^{\mathrm{fin}}_\infty$ (of finitely generated modules of finite projective dimension) over an Artin algebra is a sufficient condition for validity of finitistic dimension conjectures.
Pooyan Moradifar, Jan Šaroch
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Gorenstein Projective Dimensions of Modules over Minimal Auslander–Gorenstein Algebras [PDF]

Algebra Colloquium, 2021
In this article we investigate the relations between the Gorenstein projective dimensions of [Formula: see text]-modules and their socles for [Formula: see text]-minimal Auslander–Gorenstein algebras [Formula: see text]. First we give a description of projective-injective [Formula: see text]-modules in terms of their socles.
Li, Shen, Marczinzik, René, Zhang, Shunhua   +2 more
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Level and Gorenstein projective dimension

Journal of Algebra, 2022
We investigate the relationship between the level of a bounded complex over a commutative ring with respect to the class of Gorenstein projective modules and other invariants of the complex or ring, such as projective dimension, Gorenstein projective dimension, and Krull dimension. The results build upon work done by J. Christensen [6], H.
Laila Awadalla, Thomas Marley
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Homological dimension based on a class of Gorenstein flat modules

Comptes Rendus. Mathématique, 2023
In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek in [26].
Dalezios, Georgios, Emmanouil, Ioannis
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$\mathfrak{X}$-Gorenstein Projective Dimensions

Journal of Mathematical Study, 2022
In this paper, we mainly investigate the $\mathfrak{X}$-Gorenstein projective dimension of modules and the (left) $\mathfrak{X}$-Gorenstein global dimension of rings. Some properties of $\mathfrak{X}$-Gorenstein projective dimensions are obtained. Furthermore, we prove that the (left) $\mathfrak{X}$-Gorenstein global dimension of a ring $R$ is equal to
Wang, Jie, Xu, Xiaowei, Zhao, Zhibing
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Hilbert series, machine learning, and applications to physics

Physics Letters B, 2022
We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ∼1 mean absolute error, whilst classifiers predict dimension and Gorenstein ...
Jiakang Bao, Yang-Hui He, Edward Hirst, Johannes Hofscheier, Alexander Kasprzyk, Suvajit Majumder   +5 more
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Gillespie’s questions and Grothendieck duality

Comptes Rendus. Mathématique, 2021
Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states that “for what rings $R$ do we have $\mathrm{K}(\mathrm{AC})=\mathrm{K}(R\text{-}\mathrm{Inj})$?”. We give an answer to such a question.
Wang, Junpeng, Liu, Zhongkui, Yang, Gang
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Relative Gorenstein Dimensions over Triangular Matrix Rings

Mathematics, 2021
Let A and B be rings, U a (B,A)-bimodule, and T=A0UB the triangular matrix ring. In this paper, several notions in relative Gorenstein algebra over a triangular matrix ring are investigated.
Driss Bennis, Rachid El Maaouy, Juan Ramón García Rozas, Luis Oyonarte   +3 more
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On Gorenstein projective, injective and flat dimensions—A functorial description with applications [PDF]

Journal of Algebra, 2006
Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical counterparts, these dimensions do not immediately come with practical and robust criteria for finiteness, not even over ...
Christensen, Lars Winther, Frankild, Anders Juel, Holm, Henrik Granau   +2 more
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