| In this paper,we always assume that Г is an Artin algebra,and all r-modules,if not specified,are defaulted to left,modules.Г-mod is the catogory of all finitely generated Г-module,GP(Г)is a full subcategory of all finite generated Г-Gorenstein projective modules.In this paper,we study some good characterizations of the homological dimension on GP(Г) when GP(Г) is a weak-n-abelian category.In the first chapter,we give the background and necessary preparato-ry knowledge of Gorenstein projective modules,Gorenstein algebras and n-abelian categories(including weak-n-abelian categories).In the second chapter,we give the main results of this paper.We prove that when GP(Г) is a weak-n-abelian category,Г is an n+1 Gorenstein algebra,and that the Gorenstein projective dimension of any Г-module does not exceed n+1;the 0 order left perpendicular of Г will also be the 1 ton order left perpendicular of Г.Finally,we discuss the basic assumptions of the paper.We prove that if the weak-n-abelian category is replaced by n-abelian category in the basic hypothesis,then the GP(Г)is an n-cluster-tilting subcategory of Г-mod. |
