M431 Semigroups

Contents

  1. Summary
  2. Lecture notes
  3. Textbooks
  4. Links

1. Summary

The first part of the course consists of an introduction to the basic concepts of semigroup theory, including some of the most important classes of semigroups, such as free, regular and inverse semigroups. The second part is devoted to the theory of finite semigroups, including connections with automata and language theory. The programme of classification of finite semigroups by pseudovarieties and the role played by relatively free profinite semigroups will be presented.

2. Lecture notes

The lecture notes for the course, entitled ‘Nine Chapters on the Semigroup Art’, cover all the required material. Each chapter includes several exercises; full solutions are included.

Nine Chapters on the Semigroup Art
[ version 0.65.18 (2017-03-21)  ]
Download

3. Textbooks

All the material required for the course is included in the lecture notes. Students may wish to consult the following textbooks for further reading; copies are available in the library:

J. Almeida, Finite semigroups and universal algebra
vol. 3 in Series in Algebra. River Edge, NJ: World Scientific Publishing (1994). ISBN: 981-02-1895-8.
J.M. Howie, Fundamentals of Semigroup Theory
no. 12 in London Mathematical Society Monographs (New Series). New York: Clarendon Press, Oxford University Press (1995). ISBN: 0-19-851194-9.
J.-E. Pin, Varieties of formal languages
Foundations of Computer Science. New York: Plenum Publishing (1986). ISBN: 0-306-42294-8.

4. Links

M431 Semigroups on Sigarra: English, Portuguese.