Book:John Mackintosh Howie/An Introduction to Semigroup Theory

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