On Neutral Elements in a Lattice

Abstract

This paper deals with neutral elements and shows that it is possible to define neutrality of an element by a single equality, (i.e., a solution to problem 3 of [3] ). It also extends the theorem of J . Von Neumann that "an element of a complemented modular lattice L is neutral if and only if its complement is unique" to relatively complemented lattices, (i.e., solution to problem 16 of [3] ).