n-distributivity and n-modularity in lattices

Abstract

In this paper we consider some forbidden sublattices for n-distributive, but non-modular lattices. We define the new notion of n-modularity (weaker than n-distributivity). We also consider some forbidden sublattice for an n-modular lattice. We prove that n-modularity implies (n + 1)-modularity. The counter-examples for the inverse implication are shown.