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Speciality of full subalgebras and rational identities in Jordan algebras

Part of: Jordan algebras

Published online by Cambridge University Press:  26 February 2010

H. Essannouni  and
A. Kaidi
H. Essannouni
Affiliation:
Departement de Mathématiques et d'Informatique, Faculté des Sciences, University Mohammed V, B.P. 1014. Rabat, Morocco.
A. Kaidi
Affiliation:
Departement de Mathématiques et d'Informatique, Faculté des Sciences, University Mohammed V, B.P. 1014. Rabat, Morocco.
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Extract

The Shirshov-Cohn theorem asserts that in a Jordan algebra (with 1), any subalgebra generated by two elements (and 1) is special. Let J be a Jordan algebra with 1, a, b elements of J and let a1, a2, …, an be invertible elements of J such that

Where

are Jordan polynomials. In [2, p. 425] Jacobson conjectured that for any choice of the Pi the subalgebra of J generated by 1, a, b, a1…, an is special.

MSC classification

Secondary: 17C05: Identities and free Jordan structures
Type
Research Article
Information
Mathematika , Volume 39 , Issue 2 , December 1992 , pp. 327 - 329
Copyright
Copyright © University College London 1992

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References

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