Book:John Mackintosh Howie/An Introduction to Semigroup Theory

John Mackintosh Howie: An Introduction to Semigroup Theory

Published $\text {1976}$, Academic Press

ISBN 978-0127546339

Subject Matter

• Semigroups

Contents

Preface

Chapter I. Introductory Ideas

1. Basic definitions

2. Monogenic semigroups

3. Ordered sets, semilattices and lattices

4. Binary relations; equivalences

5. Congruences

6. Free semigroups

7. Ideals and Rees congruences

8*. Lattices of equivalences and congruences

Exercises

Chapter II. Green's Equivalences

Introduction

1. The equivalences $\mathscr L$, $\mathscr R$, $\mathscr H$, $\mathscr J$ and $\mathscr D$

2. The structure of $\mathscr D$-classes

3. Regular $\mathscr D$-classes

4. Regular semigroups

Exercises

Chapter III. $0$-Simple Semigroups

Introduction

1. Simple and $0$-simple semigroups; principal factors

2. Rees's Theorem

3. Primitive idempotents

4*. Congruences on completely $0$-simple semigroups

5*. The lattice of congruences on a completely $0$-simple semigroup

6*. Finite congruence-free semigroups

Exercises

Chapter IV. Unions of Groups

Introduction

1. Unions of groups

2. Semilattices of groups

3. Bands

4*. Free bands

5*. Varieties of bands

Exercises

Chapter V. Inverse Semigroups

Introduction

1. Preliminaries

2. The natural order relation on an inverse semigroup

3. Congruences on inverse semigroups

4. Fundamental inverse semigroups

5. Anti-uniform semigroups

6. Bisimple inverse semigroups

7. Simple inverse semigroups

8*. Representations of inverse semigroups

Exercises

Chapter VI. Orthodox Semigroups

Introduction

1. Basic properties of orthodox semigroups

2. The analogue of the Munn semigroup

3. Uniform and anti-uniform bands

4. The structure of orthodox semigroups

Exercises

Chapter VII. Semigroup Amalgams

Introduction

1. Free products

2. Diminions and zigzags

3. The embedding of amalgams

4. Inverse semigroup amalgams

Exercises

References

List of Special Symbols

Index