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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Minimal ideals in quadratic Jordan algebras
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by Seong Nam Ng and Kevin McCrimmon PDF
Proc. Amer. Math. Soc. 88 (1983), 579-583 Request permission

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
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 88 (1983), 579-583
  • MSC: Primary 17C10; Secondary 17C20
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0702278-3
  • MathSciNet review: 702278