David Stanovský    //

BINARY SYSTEMS 2013/14

25.2.	Motivation, examples. Translations, division and inverses.	notes: 1 2 3+5 4
4.3.	Semigroups: basic facts, Green's theory.	notes: 1 2 3 4 5 6 7
11.3.	Semigroups: regularity, intro to inverse semigroups.	notes
18.3.	Inverse semigroups: Vagner-Preston theorem, congruences.	notes
25.3.	Inverse semigroups: Lallement's lemma. Completely regular semigroups: an overview. Mediality: an introduction.	notes: 17A 17B 22 23 24 25
1.4.	Linearization problem. Principal isotopy, Toyoda's theorem.	notes on principal isotopy: 1 2 3 notes on mediality: 1 2 3 4 5 6 7
15.4.	Quandles: coloring knots, the structure of algebraically connected quandles.
22.4. and on	Aleš Drápal talks

HOMEWORKS --- final version.
I suggest you work all the exercices. To pass my part of the course, you need to completely solve at least half of the exercises marked [!], i.e., nine. Should you have any questions about the exercises, write me an email. In particular, if you find a wrong exercise, unclear or invalid statement, etc., please let me know.

Literature:

• John Howie: Fundamentals of Semigroup Theory (we loosely follow this book), or any other textbook on semigroups.
• A brief overview of non-associative algebra (even more motivation)
• Hala Pflugfelder: Quasigroups and loops: introduction for more details on quasigroups (medial in particular)
• a text on quandle coloring - not really good for the purposes of this lecture, but still the best I could find (let me know if you want to read more on knots, I can recommend some texts depending on your preferences)