# 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.

### 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