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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

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