Ideals In Skew Lattices

Abstract

This theses aims to develop a better understanding of skew lattice and its ideals. We present the definitions of lattice, skew lattice, ideals and filters. Due to the importance of orders and ordered sets in the study of both lattice and skew lattice, the definitions of orders and ordered sets are presented, then we de- fine a lattice in two ways and present the connection between them, furthermore, we discuss the concept of ideal and filter in a lattice. The algebraic definition of a skew lattice and some of its properties are introduced. We discuss the three Green’s relations on a skew lattice. Also we study an order structure of a skew lattice, and the related results and the characterizations theorems are studied. Furthermore we introduce the concept of ideal, filter, skew ideal and principal ideal in a skew lattice. The characterizations theorems for each of these concepts and the results connecting between them are discussed.