Over fields of characteristic not 2, noncommutative Jordan algebras are the same as
flexible Jordan-admissible algebras,[1] where a Jordan-admissible algebra – introduced by Albert (
1948) and named after
Pascual Jordan – is a (possibly
non-associative) algebra that becomes a Jordan algebra under the product a ∘ b = ab + ba.
Okubo, Susumu (1995), Introduction to octonion and other non-associative algebras in physics, Montroll Memorial Lecture Series in Mathematical Physics, vol. 2, Cambridge:
Cambridge University Press,
ISBN0-521-47215-6,
Zbl0841.17001