Approximations of injective modules and finitistic dimension

Abstract

Let Λ be an artin algebra and let the category of finitely generated right Λ-modules of finite projective dimension. We show that is contravariantly finite in if and only if the direct sum E of the indecomposable Ext -injective modules in form a tilting module in Moreover, we show that in this case E coincides with the direct sum of the minimal right -approximations of the indecomposable Λ-injective modules and that the projective dimension of E equal to the finitistic dimension of Λ.