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This analysis demonstrates the equivalence of properties of complexes in coherent rings, suggesting broader applications of acyclic complexes.
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.
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Christensen et al. (2026) studied this question.
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