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.
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1992-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171292000255 |