MATH 8090: Independent Study - Semigroup Theory (Spring 2018)

Schedule

1. 01/27: monogenic, semilattice (1.1-1.3), Thm 1.4.1, 1.5.1, 1.5.2, free semigroups, presentations (1.6), ideals, Rees quotients (1.7)
   Exercises: 1.9.7, 1.9.13, 1.9.19
2. 02/02: Green's relations 2.1-2.3 (all results with proofs)
   Exercises: 2.6.1 2.6.2, 2.6.3
3. 02/16: regular semigroups, sandwich set 2.4-2.5 (all results with proofs)
   Exercises: 2.6.10, 2.6.16, 2.6.18
4. 02/23: 0-simple semigroups 3.1-3.2.7 (with proofs), completely simple semigroups 3.3.1, 3.3.3 (without proofs), isomorphisms 3.4 (without proofs)
   Exercises: 3.8.10, 3.8.12
5. 03/02: completely regular semigroups 4.1-4.2 (with proofs), bands 4.4.1
   Exercises: 4.7.1, 4.7.8
6. 03/09: free bands 4.5 (without proofs), inverse semigroups and their order 5.1-5.2 (with proofs)
   Exercises: 4.7.21, 5.11.6
7. 03/16: free semigroups 7.1, free inverse semigroups 5.10
   Exercises: 5.11.40
8. 04/06: finitely presented semigroups CP 9.2, commutative semigroups CP 9.3 (up to Cor. 9.20)
   Exercises: CP 9.2.1, 9.3.5
9. 04/13: fg commutative semigroups are fp CP 9.3 (pp 130-136), amalgams and free products CP 9.4 (p 140-142 without proof of Thm 9.29)
   Exercises: CP 9.4.1, 9.4.5
10. 04/20: Stone-Cech compactification of a discrete semigroup HS 4.1 (focus on Theorems 4.4, 4.8)
    Exercises: HS 4.1.5, 4.1.11
11. 04/27: limits via ultrafilters HS 3.5, Ramsey Theory HS 5.1- 5.2 (up to Cor 5.10)
    Exercises: HS 3.5.2

Reading

1. Howie. Fundamentals of Semigroup Theory. Oxford University Press, 1995.
2. Clifford, Preston. The Algebraic Theory of Semigroups I, II. AMS, 1961.
3. Hindman, Strauss. Algebra in the Stone-Cech compactification. De Gruyter, 2nd edition, 2012.