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Properly algebraic and spectrum-finite ideals in Jordan systems

Published online by Cambridge University Press:  24 October 2008

Ottmar Loos
Ottmar Loos
Affiliation:
Institut für Mathematik, Universität Innsbruck, Technikerstr.25/7, A-6020 Innsbruck, Austria
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Extract

The two main results of this paper are:

(i) The set of properly algebraic elements of a Jordan system (algebra, triple system or pair) over an uncountable field is an ideal.

(ii) For a semiprimitive Banach Jordan system, the socle, the largest properly algebraic ideal, the largest properly spectrum-finite ideal and the largest von Neumann regular ideal all coincide.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 149 - 161
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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