International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 1, Pages 205-206
doi:10.1155/S0161171292000255
Remarks on derivations on semiprime rings
Mohamad Nagy Daif1
and Howard E. Bell2
1Department of Mathematics, Faculty of Education, Umm Al-Qura University, Taif, Saudi Arabia
2Department of Mathematics, Brock University, Ontario, St. Catharines, Canada
Abstract
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.