An element e in a ring R is said to be idempotent if e² = e. An element of the center of the ring R is said to be central. If e is a central idempotent in a ring R with identity, then

(a) 1_R - e is a central idempotent;

(b) eR and (1_R - e)R are ideals in R such that R = eR X (1_R - e)R.