2004•viXraRequires access
Smarandache Jordan Algebras
W. B. Vasantha, Kandasamy S. Christopher, A. Victor Devadoss
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Abstract
In this paper we assume a Jordan algebra A is one which satisfies the identity x(x 2 y) = x 2 (xy) for all x, y ∈ A. If in the Jordan algebra A, xy = yx for all x, y ∈ A we call the Jordan Algebra A to be commutative otherwise we call A a non commutative Jordan Algebra. Let Ln(m) be a special class of loops. ZLn(m) is a loop algebra which is a Jordan algebra. We define Smarandache Jordan algebras (S-Jordan algebras) and Smarandache strong Jordan algebras (S-strong Jordan algebras) and prove that a S-Jordan algebra in general is not a S-strong Jordan algebra. We also prove a S-commutative Jordan Algebra is a S-weakly commutative Jordan algebra. We define a S-Jordan algebra to be S-simple Jordan algebras if the S-Jordan algebra has no S-Jordan ideals. We obtain several other interesting notions and results on S-Jordan algebras.