Annihilators and semisimple rings Let $R$ be a semisimple ring and let $I$ be a left ideal of $R$. Denote $\text{ann}_l(S)$, resp. $\text{ann}_r(S)$, for the left (resp. right) annihilator of a left ideal $S$ of $R$. Any tips on how to show that $\text{ann}_l(\text{ann}_r(I)) \subseteq I$? 
(the reverse inclusion is straightforward)

Since $R$ is semisimple, $I=Re$ for some idempotent $e$.
It's not hard to show that $ann_r(Re)=(1-e)R$ and $ann_l(eR)=R(1-e)$.
Then $ann_l(ann_r(Re))=ann_l((1-e)R)=R(1-(1-e))=Re=I$
