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.