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fp-injective modules

Proceedings of the Edinburgh Mathematical Society (1)

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1 results

FP-injective dimensions and Gorenstein homology
Part of
- Homological algebra
Gang Yang, Junpeng Wang
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 4 / November 2022

Published online by Cambridge University Press:

21 December 2022, pp. 1183-1199
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Let $R$ be a left coherent ring. It is proven that if an $R$-module $M$ has a finite FP-injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the projective (resp. flat) dimension coincide. Also, we obtain that the pair ($\mathcal {GP},\, \mathcal {GP}^{\perp }$) forms a projective cotorsion pair under some mild conditions.