The Auslander-Bridger formula and the Gorenstein property for coherent rings

DOI10.1216/JCA-2009-1-2-283zbMath1186.13011arXiv0809.1595MaRDI QIDQ847957

Livia Hummel, Thomas Marley

Publication date: 19 February 2010

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

Full work available at URL: https://arxiv.org/abs/0809.1595

zbMATH Keywords

Gorenstein ringcoherent ringGorenstein dimension

Mathematics Subject Classification ID

Homological dimension and commutative rings (13D05) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07)

Related Items (14)

Weak Injective and Weak Flat Modules ⋮ Relative weak injective and weak flat modules with respect to a semidualizing module ⋮ The Development of Non-Noetherian Grade and Its Applications ⋮ Open Problems in Commutative Ring Theory ⋮ Stably reflexive modules and a lemma of Knudsen ⋮ \(\mathrm{FP}_n\)-injective and \(\mathrm{FP}_n\)-flat complexes ⋮ The rings in which all super finitely presented modules are Gorenstein projective ⋮ Simple \(\mathbb{Z} \)-graded domains of Gelfand-Kirillov dimension two ⋮ ALL GORENSTEIN HEREDITARY RINGS ARE COHERENT ⋮ Relative FP-gr-injective and gr-flat modules ⋮ A note on Non-Noetherian Cohen-Macaulay rings ⋮ WEAK INJECTIVE AND WEAK FLAT COMPLEXES ⋮ Super Finitely Presented Modules and Gorenstein Projective Modules ⋮ A Gorenstein analogue of a result of Bertin

Cites Work

• Non-Noetherian Cohen-Macaulay rings
• Commutative coherent rings
• Gorenstein dimensions
• Gorenstein injective and projective modules
• Proregular sequences, local cohomology, and completion
• Grade-Sensitive Modules and Perfect Modules
• Coherent rings with finite self-FP-injective dimension
• On Homological Dimensions of Rings with Countably Generated Ideals.
• Coherent Rings and Fp -Injective Modules
• Stable module theory
• The Local Rings of Global Dimension Two
• A Theory of Grade for Commutative Rings
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