Acyclic complexes and regular rings

2025/06/11 by Lars Winther Christensen, Christensen, Lars Winther, Sergio Estrada +3
Mathematics · #16E05 #16E50 #16E65 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2506.09831

openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A 2009 paper by Iacob and Iyengar characterizes noetherian regular rings in terms of properties of complexes of projective modules, flat modules, and injective modules. We show that the relevant properties of such complexes are equivalent without reference to regularity of the ring and that they characterize coherent regular rings and von Neumann regular rings.

Citations

• Homological dimensions of complexes over coherent regular rings
• A refinement of Gorenstein flat dimension via the flat--cotorsion theory
• The stable module category of a general ring
• Homological dimensions and regular rings

Related

• Homological dimensions of complexes over coherent regular rings
• Acyclicity versus total acyclicity for complexes over noetherian rings
• Totally acyclic complexes and homological invariants over arbitrary rings
• Non-Noetherian Cohen-Macaulay rings
• Relative regular modules. Applications to von Neumann regular rings