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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Quadratic Jordan algebras whose elements are all regular or nilpotent


Author: Kevin McCrimmon
Journal: Proc. Amer. Math. Soc. 45 (1974), 19-27
MSC: Primary 17A15
DOI: https://doi.org/10.1090/S0002-9939-1974-0374202-1
MathSciNet review: 0374202
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Abstract: We prove that if $ J$ is a quadratic Jordan algebra whose elements are all either regular or nilpotent, and which satisfies a common multiple property (that whenever $ z$ is nilpotent and $ \upsilon $ regular then $ \operatorname{Im} {U_\upsilon } \cap \operatorname{Ker} {U_z} \ne 0$), then modulo the radical $ R$ the algebra $ J/R$ is either a domain or a form of a Jordan algebra determined by a traceless quadratic form in characteristic 2.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0374202-1
Article copyright: © Copyright 1974 American Mathematical Society