Intro
Preface
Contents
Editors and Contributors
Ordering Orders and Quotient Rings
1 Introduction
2 Green's Relations
3 Generalized Inverses
3.1 Inverses Along an Element
3.2 Properties of the Group Inverse
4 Order Relations on General Semigroups and Their Properties
5 Quotient Rings Along Functions
5.1 Properties of Fountain-Gould Quotient Rings
6 Order Relations on a Quotient Ring
6.1 Mitsch Order Relation
6.2 Nambooripad Order Relation
6.3 Sharp Order
References
A Study on Cayley Graphs of Full Transformation Semigroups

1 Introduction
2 Preliminaries
References
Block-Groups and Hall Relations
1 Background and Motivation: Straubing's Theorem
2 Block-Groups and Power Semigroups of Groups
3 Hall Relations
4 Representation Theorem
References
Balanced Categories and the Biorder in Semigroups
1 Categories with Subobjects, Images, and the Biorders in Semigroups
1.1 Morphisms in a Category
1.2 Categories with Subobjects
1.3 Factorization of Morphisms and Categories with Images
2 The Cone Semigroup of a Category and Its Abundance

2.1 The Cone Semigroup calBC and the Idempotent Biorder of It
2.2 The Cone Semigroup calTcalC and Its Abundance
3 The Left Ideal Category of an Abundant Semigroup and Its Cone Semigroup
4 The Isomorphism Between Balanced Category calC and mathbbL(calTcalC)
References
Category of Principal Left Ideals of Normal Bands
1 Preliminaries
1.1 Normal Categories
1.2 Category of Principal Left Ideals of a Regular Semigroups
2 Normal Category from Normal Bands
2.1 Normal Bands
2.2 Category of Principal Left Ideals of Normal Bands
References

Quotients of the Booleanization of an Inverse Semigroup
1 Introduction
2 Preliminaries
2.1 First Definitions and Conventions
2.2 Representations and Proper Representations of Semilattices
2.3 The Universal Booleanization of a Semilattice
2.4 The Tight Booleanization of a Semilattice
2.5 Stone Duality for Boolean Algebras
2.6 Boolean Inverse Semigroups
2.7 Stone Groupoids
2.8 The Universal Groupoid of an Inverse Semigroup
2.9 The Tight Groupoid of an Inverse Semigroup
2.10 Stone Duality for Boolean Inverse Semigroups