Let $A$ be a finite-dimensional k-algebras, where k is a fixed field. $X$ is a finitely generated left A-module.
I have seen in a paper that "$Ext^i _A (AeA,X)=0$ is equivalent to $Ext^i _A (Y,X)=0$ for all $A/AeA$-modules $Y$ for all $0 \leq i \leq n$", where $n \in N$, $e \in A $ is an idempotent element.
I don't know why it is equivalent, can anyone help me?