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.References
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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