International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 615-618
doi:10.1155/S0161171291000844
When in a multiplicative derivation additive?
Department of Mathematics, Faculty of Education, Umm Al-Qura University, Taif, Saudi Arabia
Received 29 March 1990; Revised 19 December 1990
Copyright © 1991 Mohamad Nagy Daif. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Our main objective in this note is to prove the following. Suppose R is a
ring having an idempotent element e(e≠0, e≠1) which satisfies:
(M1) xR=0 implies x=0.(M2) eRx=0 implies x=0 (and hence Rx=0 implies x=0).(M3) exeR(1−e)=0 implies exe=0.
If d is any multiplicative derivation of R, then d is additive.