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Proceedings of the American Mathematical Society

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

 

 

Cubic subfields of exceptional simple Jordan algebras


Authors: H. P. Petersson and M. L. Racine
Journal: Proc. Amer. Math. Soc. 91 (1984), 31-36
MSC: Primary 17C40
DOI: https://doi.org/10.1090/S0002-9939-1984-0735558-7
MathSciNet review: 735558
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Abstract: Let $ E/k$ be a cubic field extension and $ J$ a simple exceptional Jordan algebra of degree 3 over $ k$. Then $ E$ is a reducing field of $ J$ if and only if $ E$ is isomorphic to a (maximal) subfield of some isotope of $ J$. If $ k$ has characteristic not 2 or 3 and contains the third roots of unity then every simple exceptional Jordan division algebra of degree 3 over $ k$ contains a cyclic cubic subfield.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0735558-7
Article copyright: © Copyright 1984 American Mathematical Society