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

 

Minimal ideals in quadratic Jordan algebras


Authors: Seong Nam Ng and Kevin McCrimmon
Journal: Proc. Amer. Math. Soc. 88 (1983), 579-583
MSC: Primary 17C10; Secondary 17C20
MathSciNet review: 702278
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Abstract: In associative and alternative algebras a minimal ideal is either trivial or simple. This is not known for quadratic Jordan algebras. In the present note we show that a minimal ideal is either trivial or $ \mathcal{D}$-simple (possesses no proper ideals invariant under all inner derivations induced from the ambient algebra). In particular, the heart of any quadratic Jordan algebra is either trivial or $ \mathcal{D}$-simple. Hearts have recently played an important role in Zelmanov's theory of prime Jordan algebras.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0702278-3
PII: S 0002-9939(1983)0702278-3
Article copyright: © Copyright 1983 American Mathematical Society