Certain additive maps on m-power closed Lie ideals
Journal
Monatshefte fur Mathematik
Journal Volume
164
Journal Issue
3
Pages
287-298
Date Issued
2011
Author(s)
Liu, K.-S.
Abstract
Let R be a prime ring with extended centroid C and m a fixed positive integer > 1. A Lie ideal L of R is called m-power closed if um ε L for all u ε L. We prove that if char R = 0 or a prime p > m, then every non-central, m-power closed Lie ideal L of R contains a nonzero ideal of R except when dimCRC = 4, m is odd, and um-1 ε C for all u ε L. Moreover, the additive maps d: L → R satisfying d(um) = mum-1d(u) (resp. d(um) = um-1d(u)) for all u ε L are completely characterized if char R = 0 or a prime p > 2(m - 1). © 2010 Springer-Verlag.
Type
journal article