Abstract
Over an artin algebra Λ, for an additive subbifunctor F of [Formula: see text] 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 Λ if and only if rel.fin.Gdim F Λ < ∞ for all artin algebras Λ.
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