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The Art of Semigroup Theory

Chances are rare, that you are reading this blog and asking the question: computational what?!? However, you may have some students interested in semigroup theory asking for some introductory material.

Standard textbooks do exist. You can start with Clifford & Preston, Howie, or Grillet, Lallement, Almeida, Eilenberg, etc. But are they available? still in print? Does your library have them? Also, do they cover the latest developments? You may end up using several monographs and some research articles, probably with slightly different notations – heavy burden on the students.

If you are a time-millionaire, then you just compile your own lecture notes. Again, chances are rare…

Alternatively, you search the Internet to check whether someone else had the time. The main idea of using the network is to promote communication and sharing and not to waste efforts on doing something that is already available. So, I searched and found this:

M431 Semigroups  Nine Chapters on the Semigroup Art


The typesetting is beautiful, both printing and ebook readers are catered for…

m431sample…and the content aims to be comprehensive. Here are the chapters.

  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

All good, I happily printed the whole book and started reading it. And then came the bad news. Some parts were flawless but other sections had numerous typos. I complied a list of typos and suggestions and emailed Alan. To my great surprise I received the answer within 24hrs, and not just the answer but a new version with corrections. Also for keeping track of the corrections, version numbers were introduced. This is a very nice situation: he gets feedback and can improve his work, and with a little effort we get the text that we can recommend to our students. Success story.

Since then there were many revisions. Although it is still a work in progress, I highly recommend these lecture notes as introductory material, the book is already in a great shape. More readers would possibly yield more comments and corrections, so we may get sooner a high-quality text, hopefully in print, maybe on a print-on-demand site.

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