Semigroups and Applications
Faculdade de Ciências e Tecnologia
Departamento de Matemática
Teacher in charge
Maria Helena Coutinho Gomes Almeida Santos, Vitor Hugo Bento Dias Fernandes
Students should get familiar with semigroup theory.
1. Basic definitions and examples. Binary relations, equivalence relations, order relations. Ideals and congruences. Homomorphisms. Free monoid and presentations. 2. Green's relations: Definitions. Structure of D-classes. Regular elements. Regular D-classes. 3. Finite semigroups: Special properties of Green’s relations. Varieties of finite semigroups definied by Green’s relations. Rees semigroups. 4 Inverse semigroups: Definition and properties. Natural order. Congruences on inverse semigroups. Representations by partial transformations. Free inverse semigroup. 5. Free monoids: Free monoids and words. Submonoids and morphisms. Conjugation. Formal series. Lyndon words. Bi-sections of monoids.
1 – Clifford,A. H. e Preston, G. B., The algebraic theory of semigroups, Amer. Math. Soc. 1967
2 – Grillet, P. A., Semigroups, Marcell Dekker, 1995
3 – Howie, J. M., Fundamentals of semigroup theory, Oxford Univ. Press, 1995
4 – Lothaire,M., Combinatorics on words, Cambridge Math. Library, 1997
5 – Pin, J. E., Varieties of formal languages, Plenum, 1986
Continuous evaluation and final essay.