WHEN IS A MULTIPLICATIVE DERIVATION ADDITIVE?

Mohamad Nagy Daif

《International Journal of Mathematics and Mathematical Sciences》 1991卷 (1991/12) Pp. 615-618

https://doi.org/10.1155/S0161171291000844

並列摘要

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:(M_1) xR=0 implies x=0. (M_2) eRx=0 implies x=0 (and hence Rx=0 implies x=0). (M_3) exeR(1-e)=0 implies exe=0. If d is any multiplicative derivation of R, then d is additive.

並列關鍵字

Ring ； idempotent element ； derivation ； Peirce decomposition