Gorenstein projective, injective and flat modules
Z Liu, X Yang - Journal of the Australian Mathematical Society, 2009 - cambridge.org
In basic homological algebra, projective, injective and flat modules play an important and
fundamental role. In this paper, we discuss some properties of Gorenstein projective …
fundamental role. In this paper, we discuss some properties of Gorenstein projective …
On Gorenstein homological dimension of groups
Y Luo, W Ren - arXiv preprint arXiv:2205.15542, 2022 - arxiv.org
Let $ G $ be a group and $ R $ be a ring. We define the Gorenstein homological dimension
of $ G $ over $ R $, denoted by ${\rm Ghd} _ {R} G $, as the Gorenstein flat dimension of …
of $ G $ over $ R $, denoted by ${\rm Ghd} _ {R} G $, as the Gorenstein flat dimension of …
Gorenstein Krull domains and their factor rings
S Xing - Communications in Algebra, 2024 - Taylor & Francis
Abstract The concept of Gorenstein Krull domains can be viewed as a Gorenstein analogue
of Krull domains, which are not necessarily integrally closed. This allows us to study those …
of Krull domains, which are not necessarily integrally closed. This allows us to study those …
Homology theories and Gorenstein dimensions for complexes
L Liang - Algebras and Representation Theory, 2021 - Springer
In this paper, we first study the Gorenstein projective/flat dimension of complexes of
modules. The relation between the Gorenstein projective/flat dimension for complexes and …
modules. The relation between the Gorenstein projective/flat dimension for complexes and …
Relative global Gorenstein dimensions
V Becerril - Journal of Algebra and Its Applications, 2022 - World Scientific
Let 𝒜 be an abelian category. In this paper, we investigate the global (𝒳, 𝒴)-Gorenstein
projective dimension gl. GPD (𝒳, 𝒴)(𝒜), associated to a GP-admissible pair (𝒳, 𝒴). We give …
projective dimension gl. GPD (𝒳, 𝒴)(𝒜), associated to a GP-admissible pair (𝒳, 𝒴). We give …
Gorenstein injective dimension, Bass formula and Gorenstein rings
L Khatami, S Yassemi - arXiv preprint math/0312513, 2003 - arxiv.org
Let $(R,\frak m, k) $ be a noetherian local ring. It is well-known that $ R $ is regular if and
only if the injective dimension of $ k $ is finite. In this paper it is shown that $ R $ is …
only if the injective dimension of $ k $ is finite. In this paper it is shown that $ R $ is …
[PDF][PDF] Finiteness aspects of Gorenstein homological dimensions
S Bouchiba - Colloq. Math, 2013 - academia.edu
We present an alternative way of measuring the Gorenstein projective (resp., injective)
dimension of modules via a new type of complete projective (resp., injective) resolutions. As …
dimension of modules via a new type of complete projective (resp., injective) resolutions. As …
[PDF][PDF] Model structures, n-Gorenstein flat modules and PGF dimensions
R El Maaouy - arXiv e-prints, 2023 - researchgate.net
Given a non-negative integer n and a ring R with identity, we construct a hereditary abelian
model structure on the category of left R-modules where the class of cofibrant objects …
model structure on the category of left R-modules where the class of cofibrant objects …
Gorenstein projective dimension relative to a semidualizing bimodule
Z Liu, Z Huang, A Xu - Communications in Algebra, 2013 - Taylor & Francis
Let S and R be rings and SCR a semidualizing bimodule. We investigate the relation
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …
[引用][C] A note on Gorenstein projective and Gorenstein flat modules
X Wang - Journal of Algebra and Its Applications, 2023 - World Scientific
We prove that all Gorenstein projective modules are Gorenstein flat if and only each
Gorenstein projective module has finite Gorenstein flat dimension. As applications, some …
Gorenstein projective module has finite Gorenstein flat dimension. As applications, some …