Let $A$ be an algebra, $J= \operatorname{rad}A$ and let $e,f$ be primitive idempotents in $A$. Given a non-zero element $a \in fJe$. Is there anyway to show that $Aa/Ja \cong Af /Jf$? Thanks.
What I have tried is as follows: Suppose $a=fje$ for some $j \in J$, define a map $g: Af \rightarrow Aa$ such that $g(m)=mje$ for $m \in Af$. There is also a canonical surjective map $\pi:Aa \rightarrow Aa/Ja$. Thus I otain a surjective homomorphism $\pi g:Af \rightarrow Aa/Ja$. But I do not know how to show $\ker(\pi g)=Jf$.