Q: Derivation and central idempotent If $D$ is a derivation of a ring $R$ and $w$ is a central idempotent. Then $D(w)$ = 0
I get $wD(w)$ = 0, but I cannot improve it.

A: Show that $wR = \{wr : r \in R\}$ is a ring with unit $w$ and that $D$ restricts to a derivation of $wR$. Now the problem is reduced to showing $D(1)=0$ for a derivation of a unital ring.
