Zahra Heidarian - Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran.

Let R be a commutative Noetherian ring. We prove that  over a local ring R every finitely generated R-module M of finite Gorenstein projective dimension has a Gorenstein projective cover\varphi:C \rightarrow M such that C is finitely generated and the projective dimension of \Ker\varphi is finite and \varphi is surjective.

Cover, Precover, Gorenstein projective, totally reflexive