PROGRESS ON THE AUSLANDER–REITEN CONJECTURE

DOI10.1017/S0004972716000071zbMath1359.14025WikidataQ123239827 ScholiaQ123239827MaRDI QIDQ2814342

Ali Mahin Fallah, Abdolnaser Bahlekeh

Publication date: 21 June 2016

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Gorenstein ringGorenstein projective modulesAuslander-Reiten conjecture

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Families, moduli of curves (algebraic) (14H10) Syzygies, resolutions, complexes and commutative rings (13D02) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07)

Cites Work

• On algebras with complete homology
• Modules without self-extensions and Nakayama's conjecture
• When are torsionless modules projective?
• Algebras that satisfy Auslander's condition on vanishing of cohomology.
• Gorenstein dimensions
• On a conjecture of Auslander and Reiten
• Gorenstein injective and projective modules
• On the Auslander-Reiten conjecture for algebras
• Liftings and weak liftings of modules
• Auslander-Reiten conjecture and Auslander-Reiten duality
• The Auslander-Reiten conjecture for Gorenstein rings
• Gorenstein dimension and proper actions
• Vanishing of cohomology over Gorenstein rings of small codimension

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