Flexible Algebras of Degree Two
Joseph H. Mayne · Transactions of the American Mathematical Society · 1972
All known examples of simple flexible power-associative algebras of degree two are either commutative or noncommutative Jordan. In this paper we construct an algebra which is partially stable but not commutative and not a noncommutative Jordan algebra. We then investigate the multiplicative structure of those algebras which are partially stable over an algebraically closed field of characteristic $p e 2,3,5$. The results obtained are then used to develop conditions under which such algebras must be commutative.