On F-Gorenstein dimensions

摘要

Over an artin algebra A, for an additive subbifunctor F of Ext_Λ~1(,) with enough projectives and injectives, we introduce F-Gorenstein dimensions in this paper. The new relative dimensions are useful to characterize F-Gorenstein algebras and F-self-injective algebras. In addition, with the aid of F-Gorenstein dimensions, we obtain an equivalent condition for the finitistic dimension conjecture to hold, that is, fin.dim Λ < ∞ for all artin algebras A if and only if rel.fin.Gdim F A < ∞ for all artin algebras Λ.