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
