Characterizing When the Category of Gorenstein Projective Modules is an Abelian Category

Abstract

We find sufficient and necessary conditions for the category of Gorenstein projective modules of an artin algebra being an abelian category, and give another proof for the Auslander–Solberg correspondence which demonstrates the concrete form of the category of Gorenstein projective modules. Then we find a characterization for this category of Gorenstein projective modules. At last we give an example of this correspondence.