Related pagesMoufang planes
Lenz type VI
for alle elements a,b in K. The alternative fields are exactly the ternary fields coordinatizing Moufang planes. In fact, the following theorem holds.
Theorem. A ternary field (K,T) is an alternative field if and only if the projective plane P(K,T) over K is a Moufang plane.
Given any alternative field K, the following algebraic facts are known.
Theorem. Let K be an alternative field. Then either K is a skewfield or K is an eight-dimensional octonion algebra over it's center Z(K).