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Nodal Non-Commutative Jordan Algebras

Published online by Cambridge University Press:  20 November 2018

Louis. A. Kokoris
Louis. A. Kokoris*
Affiliation:
Illinois Institute of Technology
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A finite dimensional power-associative algebra 𝒰 with a unity element 1 over a field J is called a nodal algebra by Schafer (7) if every element of 𝒰 has the form α1 + z where α is in J, z is nilpotent, and if 𝒰 does not have the form 𝒰 = ℐ1 + n with n a nil subalgebra of 𝒰. An algebra SI is called a non-commutative Jordan algebra if 𝒰 is flexible and 𝒰+ is a Jordan algebra. Some examples of nodal non-commutative Jordan algebras were given in (5) and it was proved in (6) that if 𝒰 is a simple nodal noncommutative Jordan algebra of characteristic not 2, then 𝒰+ is associative. In this paper we describe all simple nodal non-commutative Jordan algebras of characteristic not 2.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 488 - 492
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Albert, A.A., On commutative power-associative algebras of degree two, Trans. Amer. Math. Soc, 74 (1953), 323–343.Google Scholar
2. Harper, L.R., Some properties of partially stable algebras, University of Chicago Ph.D. dissertation.Google Scholar
3. Jacobson, N., Classes of restricted Lie algebras of characteristic p. II, Duke Math. J., 10 (1943), 107–121.Google Scholar
4. Jacobson, N., A theorem on the structure of Jordan algebras, Proc. Nat. Acad. Sci. U.S.A., 42 (1956), 140–147.Google Scholar
5. Kokoris, L.A., Some nodal noncommutative Jordan algebras, Proc. Amer. Math. Soc, 9 (1958), 164–166.Google Scholar
6. Kokoris, L.A., Simple nodal noncommutative Jordan algebras. Proc. Amer. Math. Soc, 9 (1958), 652–654.Google Scholar
7. Schafer, R.D., On noncommutative Jordan algebras, Proc. Amer. Math. Soc, 9 (1958), 110–117.Google Scholar