On idempotent elements that are contained in center of a ring Let $e$ and $f$ be idempotent elements of a ring $R$. Assume that $e,f$ are contained in center of $R$. Show that $Re=Rf$ if and only if $e=f$ 
Help me a hint to prove it.
Thank in advanced.

HINT : show that the sum and product of $R$ induce a sum and product on $Re$. What can you say about $e\in Re$ with respect to multiplication?
