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: for all positive integers m and n.