Strongly Gorenstein projective, injective and flat modules.

DOI10.1016/j.jalgebra.2008.07.006zbMath1173.16006OpenAlexW2011188222WikidataQ123290821 ScholiaQ123290821MaRDI QIDQ958051

Xiao Yan Yang, Liu, Zhongkui

Publication date: 2 December 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2008.07.006

zbMATH Keywords

Morita equivalencescompletionsMatlis dualitylocalizationsGorenstein flat modulesGorenstein injective modulesexcellent extensionsstrongly Gorenstein projective modules

Mathematics Subject Classification ID

Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Syzygies, resolutions, complexes in associative algebras (16E05) Other classes of modules and ideals in associative algebras (16D80)

Related Items (24)

G_C-PROJECTIVE, INJECTIVE AND FLAT MODULES UNDER CHANGE OF RINGS ⋮ Strongly Gorenstein categories ⋮ \textit{SG}-flat complexes and their generalizations ⋮ Strongly Gorenstein graded modules ⋮ Noncommutative G-semihereditary rings ⋮ On strongly Gorenstein hereditary rings ⋮ Gorenstein FC-projective modules ⋮ n-Strongly Gorenstein Projective and Injective Complexes ⋮ The finitely presented torsion-free SG-projective modules are not necessarily projective ⋮ Strongly \(\mathcal{E}\)-Gorenstein injective and flat modules ⋮ $W$-Gorenstein objects in triangulated categories ⋮ Strongly Gorenstein-projective quiver representations ⋮ \(K_0\) and rings over which the class of finitely generated strongly Gorenstein projective modules is closed under extensions. ⋮ Relative stable (co)homology ⋮ Representations of quivers over Artinian rings ⋮ Gillespie's questions and Grothendieck duality ⋮ Strongly \((\mathscr{X},\mathscr{Y},\mathscr{Z})\)-Gorenstein modules and applications ⋮ $n$-strongly Gorenstein graded modules ⋮ n-Strongly Gorenstein Projective, Injective and Flat Modules ⋮ Gorenstein Flat and Cotorsion Dimensions of Unbounded Complexes ⋮ On Strongly Gorenstein FP-Injective Modules ⋮ Unnamed Item ⋮ Strongly W-Gorenstein modules ⋮ A note on Gorenstein AC-projective and Gorenstein AC-flat modules

Cites Work

• Unnamed Item
• Unnamed Item
• It's essentially Maschke's theorem
• On Gorenstein projective, injective and flat dimensions -- a functorial description with applications
• Gorenstein homological dimensions and Auslander categories
• Strongly Gorenstein projective, injective, and flat modules
• Finite normalizing extensions
• Gorenstein homological dimensions.
• Gorenstein dimensions
• Flat covers of modules
• Gorenstein injective and projective modules
• Relative homological algebra
• Modules with decompositions that complement direct summands
• On gorenstein injective modules
• ABSOLUTE, RELATIVE, AND TATE COHOMOLOGY OF MODULES OF FINITE GORENSTEIN DIMENSION
• Observations on group rings
• A Theorem of Burnside on Matrix Rings
• Injective Dimension in Noetherian Rings
• Stable module theory

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