Related pagesMoufang planes
The plane P(K,T) over a ternary field (K,T) is a translation plane with respect to the line at infinity if and only if (K,T) is a quasifield.
An affine plane is called an affine translation plane if it's projective closure is a translation plane with respect to the line at infinity.
Given a vector space V over a skewfield K, and a spread S, then we may define an affine translation plane as follows. Points of are the points of V, and the lines of are defined to be the subsets of the form t+U where t is an element of V and All affine translation planes are of this form, up to isomorphism.