A Study on Finitely Generated N-Ideals of a Lattice

Abstract

This thesis studies extensively the finitely generated n-ideals of a lattice. The idea of n-ideals in a lattice was first introduced by Cornish and Noor in studying the kernels around a particular element n, of a skeletal congruence on a distributive lattice. Then Latif in his thesis "n-ideals of a lattice" studied thoroughly on the n-ideals and established many valuable results. For a fixed element n of a lattice L, a convex sub lattice of L containing n is called an n-ideal. If L has a "O", then replacing n by 0, an n-ideal becomes an ideal and if L has a "1" then it becomes a filter by replacing n by 1. Thus, the idea of n-ideals is a kind of generalization of both ideals and filters of lattices. The n-ideal generated by a finite number of elements of a lattice is called a finitely generated n-ideal, while the n-ideal generated by a single. element is known as a principal n-ideal. Latif in his thesis has given a neat description on finitely generated n-ideals of a lattice a'nd has provided a number of important results on them.