0-Conditions in the Lattice of Convex Sublattices

Abstract

In this paper, it is proved that if the lattice of all convex sublattices of a given lattice  is respectively 0-modular,0-distributive,0-supermodular,0-semi modular, super-0-distributive, pseudo-0-distributive, Eulerian, General disjointness condition, then  is also 0-modular,0-distributive,0-supermodular,0-semi modular, super-0-distributive, pseudo-0-distributive, Eulerian and satisfies General disjointness condition, then  also posses the same property.