Linear identities and derivations
Journal
Communications in Algebra
Journal Volume
28
Journal Issue
7
Pages
3317-3327
Date Issued
2000
Author(s)
Shiue, W.-K.
Abstract
Applying a result concerning generalized linear identities on prime rings, we prove a theorem on derivations: Let R be a prime ring with extended centroid C, dimC RC > 4, L a noncommutative Lie ideal of R and δ a derivation of R. Suppose that Σni=0 aixδi ∈ C for all x ∈ L, where the ai's are fixed elements in R. Then Σni=0 aixδi = 0 for all x ∈ R.
Type
journal article