The Orthogonal Complement Relative to the Functor Extension of the Class of all Gorenstein Projective Modules

Abstract

In this paper, we study the pair $(\mathcal {G}P(R),\mathcal {G}P(R)^{\perp})$ where $\mathcal{G}P(R)$ is the class of all Gorenstein projective modules. We prove that it is a complete hereditary cotorsion theory, provided $l. {\rm Ggldim}(R)< \infty$. We discuss also, when every Gorenstein projective module is Gorenstein flat.