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Speciality of full subalgebras and rational identities in Jordan algebras

  • H. Essannouni (a1) and A. Kaidi (a1)

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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.

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References

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1.Essannouni, H.Garijo, P. JiminezKaidi, A. and Palacios, A. Rodriguez. Rational identities in Jordan algebra. Algebras Groups Geom., 5 (1988), 411420.
2.Jacobson, N.. Structure and representation of Jordan algebras. Amer. Math. Soc. Coll. Publ 39 (Providence, Rhode Island, 1968).
3.Martindale, W. S. and McCrimmon, K.. Imbedding nondegenerate Jordan algebras in semiprimitive algebras. Proc. Amer. Math. Soc., 103 (1988), 10311036.
4.Moreno, J. Martinez. Sobre algebras de Jordan normadas completas. Tesis doctoral (Univ. de Granada, 1977).
5.McCrimmon, K.. Macdonald's theorem with inverses. Pacific J. Math., 21 (1967), 315325.
6.McCrimmon, J.. The radical of Jordan algebras. Proc. Nat. Acad. Sci. U.S.A., 62 (1969), 671678.
7.Zelmanov, E.. On prime Jordan algebras II. Siberian, Math. J., 24 (1983).
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Speciality of full subalgebras and rational identities in Jordan algebras

  • H. Essannouni (a1) and A. Kaidi (a1)

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