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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Middle nucleus=center in semiprime Jordan algebras


Authors: Kevin McCrimmon and Seong Nam Ng
Journal: Proc. Amer. Math. Soc. 86 (1982), 21-24
MSC: Primary 17C10
MathSciNet review: 663858
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Abstract: A. A. Albert showed that the middle nucleus and center coincide for a simple Jordan algebra finite-dimensional over a field of characteristic $ \ne 2$. E. Kleinfeld extended this to arbitrary simple Jordan algebras of characteristic $ \ne 2$. Recently this result has played a crucial role in the structure theory of E. Zelmanov. In this note we extend the result to linear Jordan algebras with no derivation-invariant trivial ideals.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0663858-6
PII: S 0002-9939(1982)0663858-6
Article copyright: © Copyright 1982 American Mathematical Society