Ad-nilpotent Elements of Semiprime Rings with Involution
Journal
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques
Journal Volume
61
Journal Issue
2
Pages
318-327
Date Issued
2018
Author(s)
Abstract
Abstract Let R be an n !-torsion free semiprime ring with involution * and with extended centroid C , where n > 1 is a positive integer. We characterize a ? K , the Lie algebra of skew elements in R , satisfying (ad a ) n = 0 on K . This generalizes both Martindale and Miers�� theorem and the theorem of Brox et al. In order to prove it we first prove that if a, b ? R satisfy (ad a ) n = ad b on R , where either n is even or b = 0, then ( a ? �f ) [(n+1)/2] = 0 for some �f ? C .