FP-injective dimensions and Gorenstein homology

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.