Structured theorems for relatively complemented lattices
Jack McLaughlin · Pacific Journal of Mathematics · 1953
Introduction.In a previous paper [3J a study was made of the projectivities between the points of a simple relatively complemented lattice of finite dimension.It was shown that for a given dimension there is an upper bound for the number of transposes required to establish the projectivities between the points.The examples given in which this upper bound is attained have a particularly simple structure -they are closely related to a direct union.We shall prove here some general structure theorems for relatively complemented lattices and then apply these to the case of maximal projectivities.The notation will be that of [3l The lattice L to which we refer is always relatively complemented.