Math 8090 Spring 18

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

Meeting: Friday, 10-11 am, Math 310

Schedule

Section numbers refer to Howie H, Clifford-Preston CP, Hindman-Strauss HS, respectively
  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

The following books are available in Gemmill library.
  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.