On Stability of Gorenstein Categories

DOI10.1080/00927872.2012.677892zbMath1284.16006OpenAlexW1981805037MaRDI QIDQ2850826

Aimin Xu, Nan Qing Ding

Publication date: 30 September 2013

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

Full work available at URL: https://doi.org/10.1080/00927872.2012.677892

zbMATH Keywords

Gorenstein flat modulesGorenstein projective modulesGorenstein complexes

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) Resolutions; derived functors (category-theoretic aspects) (18G10) Syzygies, resolutions, complexes in associative algebras (16E05) Relative homological algebra, projective classes (category-theoretic aspects) (18G25) Homological dimension in associative algebras (16E10)

Related Items (11)

Cartan-Eilenberg Gorenstein-injective \(m\)-complexes ⋮ On the stability question of Gorenstein categories ⋮ The right Gorenstein subcategory \(r\mathcal{G}(\mathscr{C},\mathscr{D})\) ⋮ Gorenstein global dimensions relative to balanced pairs ⋮ $VW$-Gorenstein complexes ⋮ Gorenstein objects in the category of N-complexes ⋮ Cartan-Eilenberg Gorenstein projective N-complexes ⋮ Resolutions and stability of Gorenstein classes of modules ⋮ (𝒲,𝒴,𝒳)-Gorenstein complexes ⋮ Gorenstein projective complexes with respect to cotorsion pairs ⋮ Gorenstein flat modules with respect to duality pairs

Cites Work

• Unnamed Item
• \(\mathcal W\)-Gorenstein modules
• Strongly Gorenstein projective, injective, and flat modules
• Homological dimensions of unbounded complexes
• Flat covers of complexes
• Gorenstein homological dimensions.
• Gorenstein injective and projective modules
• Relative homological algebra
• Approximations and endomorphism algebras of modules.
• Gorenstein Projective, Injective, and Flat Complexes
• n-Strongly Gorenstein Projective, Injective and Flat Modules
• Rings Over Which the Class of Gorenstein Flat Modules is Closed Under Extensions
• A GENERALIZATION OF STRONGLY GORENSTEIN PROJECTIVE MODULES
• Gorenstein injective and projective complexes
• The flat model structure on 𝐂𝐡(𝐑)
• Stability of Gorenstein categories
• Stable module theory

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