The Gorenstein Projective Modules Are Precovering

The Gorenstein projective modules are proved to form a precovering class in the module category of a ring which has a dualizing complex. 0. Introduction This paper proves over a wide class of rings that the Gorenstein projective modules form a precovering class in the module category. Let me explain this statement. There are two terms of mystery, “Gorenstein projective modules” and “precovering class”; I will explain the latter first. Precovering classes are also known by the name of contravariantly finite classes. In a module category, a class G of modules is precovering if is satisfies the following: For each module M , there exists a homomorphism G −→ M with G in G, such that if G̃ −→ M is any homomorphism with G̃ in G then the dotted arrow exists to make the following diagram commutative, G .. .. .. .. .. .. ..