A nonassociative algebra named after physicist Pascual Jordan which satisfies
(1)

and
(2)

The latter is equivalent to the socalled Jordan identity
(3)

(Schafer 1996, p. 4). An associative algebra with associative product can be made into a Jordan algebra by the Jordan product
(4)

Division by 2 gives the nice identity , but it must be omitted in characteristic .
Unlike the case of a Lie algebra, not every Jordan algebra is isomorphic to a subalgebra of some . Jordan algebras which are isomorphic to a subalgebra are called special Jordan algebras, while those that are not are called exceptional Jordan algebras.