Structured theorems for relatively complemented lattices

Abstract

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.