MULTIPLICATIVE GENERALIZED DERIVATIONS WHICH ARE ADDITIVE

Abstract

The purpose of this note is to prove the following. Suppose R is a ring having an idempotent element e (e = 0, e= 1) which satisfies some conditions. If g is any multiplicative generalized derivation of R, i.e. g(xy)=g(x)y +xd(y), for all x,y in R and some derivation d of R, then g is additive.