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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<ref>Jacobson (1968),
Jordan algebras were first introduced by {{harvstxtauthorlink=Pascual Jordanfirst=Pascual last=Jordanyear=1933}} to formalize the notion of an algebra of [[observable]]s in [[quantum mechanics]]. They were originally called "rnumber systems", but were renamed "Jordan algebras" by {{harvstxtauthorlink=Abraham Adrian Albertlast=Albertfirst=Abraham Adrianyear=1946}}, who began the systematic study of general Jordan algebras.
