Nine Chapters on the Semigroup Art
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Summary

These are lecture notes for a tour through selected areas of semigroup theory. There are essentially three parts:

The course is broad rather than deep. It is not intended to be comprehensive: it does not try to study (for instance) structure theory as deeply as Howie, Fundamentals of Semigroup Theory, pseudovarieties as deeply as Almeida, Finite Semigroups and Universal Algebra, or languages as deeply as Pin, Varieties of Formal Languages; rather, it samples highlights from each area. It should be emphasized that there is very little that is original in this course. It is heavily based on the treatments in these and other standard textbooks, as the bibliographic notes in each chapter make clear. The main novelty is in the selection and arrangement of material, the slightly slower pace, and the general policy of avoiding leaving proofs to the reader when the corresponding results are required for later proofs.

Chapter titles
  1. Elementary semigroup theory
  2. Free semigroups & presentations
  3. Structure of semigroups
  4. Regular semigroups
  5. Inverse semigroups
  6. Commutative semigroups
  7. Finite semigroups
  8. Varieties & pseudovarieties
  9. Automata & finite semigroups

Note: These notes were heavily revised in 2013–15. Most of the main text is now stable, but Chapter 8 will be further revised, and further exercises will be added. The author welcomes any corrections, observations, or constructive criticisms; please send them to the email address on the copyright page. At present, the index is limited to Chapter 1, plus names and ‘named results’.

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