Jordan algebra

Noun

Meaning

Jordan algebra (plural Jordan algebras)

(mathematics) A non-associative algebra over a field whose product satisfies the axioms (i)



x
y
=
y
x


{\displaystyle xy=yx}

(the commutative law) and (ii)



(
x
y
)
(
x
x
)
=
x
(
y
(
x
x
)
)


{\displaystyle (xy)(xx)=x(y(xx))}

(the Jordan identity).

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