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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  and
C. Robert Miers
W. S. Martindale 3rd
Affiliation:
Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003, USA
C. Robert Miers
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3P4
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Abstract

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Let R be a prime ring with invoution *, of characteristic 0, with skew elements K and extended centroid C. Let a ∈ K 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).

Keywords

16A1216A2816A72
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 5 , 01 October 1991 , pp. 1045 - 1054
Copyright
Copyright © Canadian Mathematical Society 1991

References

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