Contravariant Finiteness of Modules of Finite Gorenstein Projective Dimension

摘要

Let A be an artin algebra. In this paper, we give a sufficient condition for the subcategory GP ∞(A) of A -mod to be contravariantly finite in A -mod, where GP ∞(A) is the subcategory of A -mod consisting of A -modules of finite Gorenstein projective dimension. As an application of this condition it is shown that GP ∞(A) is contravariantly finite in A -mod when A is stably equivalent to a hereditary algebra.