Partial complementation on distributive lattices

The notion of partial complementation of distributive lattices is introduced. Certain important properties of partially complemented distributive lattices are investigated. Some equivalent conditions are given for every partially complemented lattice to become a demi-complemented lattice. The independency between the class of all partially complemented lattices and the other classes of lattices such as pseudo-complemented lattices and [Formula: see text]-algebras is studied. The notion of skew-complemented lattices is introduced and a necessary and sufficient condition is derived for every lattice to become a skew-complemented lattice.