Moufang plane

In geometry, a Moufang plane, named for Ruth Moufang, is a type of projective plane, more specifically a special type of translation plane.

[3] This theorem states that a restricted form of Desargues' theorem holds for every line in the plane.

[5] In algebraic terms, a projective plane over any alternative division ring is a Moufang plane,[6] and this gives a 1:1 correspondence between isomorphism classes of alternative division rings and of Moufang planes.

As a consequence of the algebraic Artin–Zorn theorem, that every finite alternative division ring is a field, every finite Moufang plane is Desarguesian, but some infinite Moufang planes are non-Desarguesian planes.

In particular, the Cayley plane, an infinite Moufang projective plane over the octonions, is one of these because the octonions do not form a division ring.