Chopped Lattices

Abstract

The first basic technique is the use of a chopped lattice, a finite meet-semilattice 〈M,∧〉 regarded as a partial algebra 〈M,∧,∨〉, where ∨ is a partial operation. It turns out that the ideals of a chopped lattice form a lattice with the same congruence lattice as that of the chopped lattice. So to construct a finite lattice with a given congruence lattice it is enough to construct such a chopped lattice. The problem is how to ensure that the ideal lattice of the chopped lattice has some given properties. As an example, we will look at sectionally complemented lattices.