Types of Lattices and Applications of Complete Lattices

Abstract

This thesis aims to develop a better understanding of lattices. P] presents lattices, types of lattices and discusses three applications of complete lattices. Due to the importance of orders and ordered sets ]% study lattices, this thesis looks first at definitions and some examples of orders and ordered sets, then it defines a lattice in two ways and connects between the two definitions. This thesis then exposes some types of lattices with both important properties to each type and useful theories ]% determine the type of a given lattices. Complete lattices, as a type of lattices have several applications in science. This thesis presents three applications of complete lattices hP] discusses the impact of retraction operator on a complete lattices , the existence of a fixed point of decreasing functions defined on a complete lattices, and finally this thesis defines the annihilator of a subset and discuss when this annihilator can be an associated prime ideals of complete lattices