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FP-injective dimensions and Gorenstein homology
Published online by Cambridge University Press: 21 December 2022
Abstract
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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 4 , November 2022 , pp. 1183 - 1199
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society