Jordan algebra

In abstract algebra, a Jordan algebra is an (nonassociative) algebra over a field whose multiplication satisfies the following axioms:

The product of two elements x and y in a Jordan algebra is also denoted x ∘ y, particularly to avoid confusion with the product of a related associative algebra. The axioms imply that a Jordan algebra is power-associative and satisfies the following generalization of the Jordan identity: $(x^my)x^n = x^m(yx^n)$ for all positive integers m and n.

单词	Jordan algebra
释义	Jordan algebra 英语百科 Jordan algebra In abstract algebra, a Jordan algebra is an (nonassociative) algebra over a field whose multiplication satisfies the following axioms: The product of two elements x and y in a Jordan algebra is also denoted x ∘ y, particularly to avoid confusion with the product of a related associative algebra. The axioms imply that a Jordan algebra is power-associative and satisfies the following generalization of the Jordan identity: $(x^my)x^n = x^m(yx^n)$ for all positive integers m and n.
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