Abstract
Given an Ext-injective stratifying system of Λ -modules ( θ , Y ̲ , ≼ ) satisfying that the projective dimension of Y is finite, we prove that the finitistic dimension of the algebra Λ is equal to the finitistic dimension of the category I ( θ ) = { X ∈ mod Λ : Ext Λ 1 ( -, X ) | F ( θ ) = 0 } . Moreover, using the theory of stratifying systems we obtain bounds for the finitistic dimension of Λ . In particular, we get the optimal bound 2 n - 2 for the finitistic dimension of a standardly stratified algebra with n simples.
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