期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1991
卷号：14
DOI：10.1155/S0161171291000844
出版社：Hindawi Publishing Corporation
摘要：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.
