GORENSTEIN INJECTIVE AND PROJECTIVE COMPLEXES

In this article we extend the notion of Gorenstein injective and proje ctive modules to that of complexes and characterize such complexes. We prove that over an a-Gorenstein ring every complex has a Gorenstein i njective envelope and we show that every such envelope is a quasi-isom orphim. When the ring is commutative, local and Gorenstein, Auslander announced that every finitely generated R-module has a finitely genera ted Gorenstein projective cover. We show that every bounded above comp lex having all terms finitely generated over such a ring has a Gorenst ein projective cover and we show that these covers are quasi-isomorphi sms.