Remarks on derivations on semiprime rings

Remarks on derivations on semiprime rings

We prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) xy+d(xy)=yx+d(yx) for all x, y in R, or (ii) xy−d(xy)=yx−d(yx) for all x, y in R. In the event that R is prime, (i) or (ii) need only be assumed for all x, y in some nonzero ideal of R.

Bibliographic Details
Main Authors: Mohamad Nagy Daif, Howard E. Bell
Format: Article
Language:English
Published: Hindawi Limited 1992-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
derivation
semiprime ring
prime ring
commutative
central ideal
integral domain
direct sum.
Online Access:http://dx.doi.org/10.1155/S0161171292000255
Description
Summary:We prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) xy+d(xy)=yx+d(yx) for all x, y in R, or (ii) xy−d(xy)=yx−d(yx) for all x, y in R. In the event that R is prime, (i) or (ii) need only be assumed for all x, y in some nonzero ideal of R.
ISSN:0161-1712
1687-0425

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