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A Note on Nilpotent Jordan Rings

Published online by Cambridge University Press:  20 November 2018

Wallace S. Martindale III
Wallace S. Martindale III*
Affiliation:
University of Massachusetts Amherst, MA 01003, U.S.A. University College London, LondonWCIE 6BT
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Abstract

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Let R be a 2-torsion free associative ring with involution. It is shown that if the set S of symmetric elements is nilpotent as a Jordan ring then R is nilpotent.

Keywords

16A68
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 399 - 401
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Martindale, Wallace S. III and Susan, Montgomery, Fixed elements of Jordan automorphisms of associative rings, Pac. J. Math. 72 (1977), pp. 181–196.Google Scholar
2. Schafer, Richard D., An introduction to nonassociative algebras, Academic Press, New York and London, 1966.Google Scholar