n-Distributive Lattice

Abstract

J. C. Varlet has given the concept of 0-distributive and 1-distributive lattices. In this paper the authors have generalized the whole concept and introduced the notion of n-distributive lattices. They show that for a neutral element of a lattice L , the nannihilator of any subset of L is an n-ideal if and only if L is n-distributive. Then the authors study different properties of these lattices. Finally, using the nannihilators they generalize the well known prime Separation theorem of distributive lattices with respect to annihilator n-ideal in a general lattice and produce an interesting characterization of n-distributive lattice.