The existence totally reflexive covers

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.

کلیدواژه ها:

Cover ، Precover ، Gorenstein projective ، totally reflexive