Structure, symmetry and graphs of inverse LA-semigroups

Abstract

In this chapter, we provide general information for the rest of the thesis. The essential de ni- tions and results regarding LA-semigroups are presented here. The chapter is divided into four sections. The areas covered here are magmas in general, LA-semigroups in particular. Similar algebraic concepts regarding semigroups are available in books such as Fundamentals of Semi- group Theory [24] by Howie, The Algebraic Theory of Semigroups [8] by Cli¤ord and Preston, and Theory of Partial Symmetries [34] by Lawson. The purpose of this chapter is to enable the readers to comprehend this work without consulting the references. However, references for more knowledge are provided throughout. Besides introducing the fundamental concepts of LA-semigroups that are available in existing literature, the chapter also provides some new ideas.