A note on derivations in semiprime rings

作者：Joso Vukman; Irena Kosi Ulbl

来源：International Journal of Mathematics and Mathematical Sciences, 2005.

DOI：10.1155/ijmms.2005.3347

We prove in this note the following result. Let n%26#62;1 be an integer and let R be an n!-torsion-free semiprime ring with identity element. Suppose that there exists an additive mapping D:R%26#8594;R such that D(xn)=%26#8721;j=1nxn%26#8722;jD(x)xj%26#8722;1 is fulfilled for all x%26#8712;R. In this case, D is a derivation. This research is motivated by the work of Bridges and Bergen (1984). Throughout, R will represent an associative ring with center Z(R). Given an integer n%26#62;1, a ring R is said to be n-torsion-free if for x%26#8712;R, nx=0 implies that x=0. Recall that a ring R is prime if for a,b%26#8712;R, aRb=(0) implies that either a=0 or b=0, and is semiprime in case aRa=(0) implies that a=0. An additive mapping D:R%26#8594;R is called a derivation if D(xy)=D(x)y

• 出版日期2005