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arXiv · 2409.08393

Homological dimensions of complexes over coherent regular rings

James Gillespie·Alina Iacob
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Abstract

We show that Iacob-Iyengar's answer to a question of Avromov-Foxby extends from Noetherian to coherent rings. In particular, a coherent ring R is regular if and only if the injective (resp. projective) dimension of each complex X of R-modules agrees with its graded-injective (resp. graded-projective) dimension. The same is shown for the analogous dimensions based on FP-injective R-modules, and on flat R-modules.

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James Gillespie, Alina Iacob. 2024-09-12. Homological dimensions of complexes over coherent regular rings. https://arxiv.org/abs/2409.08393

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