A result on derivations
Journal
Proceedings of the American Mathematical Society
Journal Volume
124
Journal Issue
6
Pages
1687-1691
Date Issued
1996
Author(s)
Lin, J.-S.
Abstract
Let A be a semiprime ring with a derivation d and let U be a Lie ideal of R, a ∈ R. Suppose that ad(u)n = 0 for all u ∈ U, where n is a fixed positive integer. Then ad(I) = 0 for I the ideal of R generated by [U,U] and if R is 2-torsion free, then ad(U) = 0. Furthermore, R is a subdirect sum of semiprime homomorphic images R1 and R2 with derivations d1 and d2, induced canonically by d, respectively such that ād1(R1) = 0 and the image of U in R2 is commutative (central if R is 2-torsion free), where ā denotes the image of a in R1. Moreover, if U = R, then ad(R) = 0. This gives Bresar's theorem without the (n - 1)!-torsion free assumption on R. © 1996 American Mathematical Society.
Type
journal article