When in a multiplicative derivation additive?

Mohamad Nagy Daif

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-4

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: ( M 1 ) x R = 0 implies x = 0. ( M 2 ) e R x = 0 implies x = 0 ( and hence R x = 0 implies x = 0 ) . ( M 3 ) e x e R ( 1 − e ) = 0 implies e x e = 0. If d is any multiplicative derivation of R , then d is additive.

Date: 1991
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/14/275743.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/14/275743.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:275743

DOI: 10.1155/S0161171291000844

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().