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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
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 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).

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1991

References

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3. Lanski, C., Differential identities in prime rings with involution, TAMS 292 (1985), 765787.Google Scholar
4. Martindale, W.S., Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576584.Google Scholar
5. Martindale, W.S., Lie isomorphisms of prime rings, Trans. Amer. M. Soc. 142 (1969), 437455.Google Scholar
6. Martindale, W.S., Lectures at Jilen University. University of Massachusetts, unpublished.Google Scholar
7. Martindale, W.S. and Miers, C.R., On the iterates of derivations of prime rings, Pac. J. Math. 104 (1983), 179190.Google Scholar
8. Martindale, W.S. and Miers, C.R., Herstein s Lie theory revisited, J. Algebra 98 (1986), 1437.Google Scholar
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