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Nilpotent Inner Derivations of the Skew Elements of Prime Rings With Involution

Published online by Cambridge University Press:  20 November 2018

W. S. Martindale 3rd
Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003, USA
C. Robert Miers
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3P4
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Let R be a prime ring with invoution *, of characteristic 0, with skew elements K and extended centroid C. Let aK be such that (ad a)n =0 on K. It is shown that one of the following possibilities holds: (a) R is an order in a 4-dimensional central simple algebra, (b) there is a skew element λ in C such that , (c) * is of the first kind, n ≡ 0 or n ≡ 3 (mod 4), and . Examples are given illustrating (c).


Research Article
Copyright © Canadian Mathematical Society 1991


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