Topics of Semigroups
Code
11696
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Vitor Hugo Bento Dias Fernandes
Weekly hours
4
Total hours
56
Teaching language
Português
Subject matter
1. Regular semigroups: general properties, the Petrich representation; strict regular semigroups; Clifford semigroups, free bands; varieties of bands.
2. Inverse semigroups: general properties; fundamental inverse semigroups, bisimple inverse semigroups; unitary covers; the McAlister P-theorem; free inverse semigroups.
3. Some Classes of Regular Semigroups: locally inverse semigroups, regular semigroups generated by idempotents; orthodox semigroups; pseudoinverse semigroups; E-unitary regular semigroups and Szendrei P-theorem.
Bibliography
1. Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Amer. Math. Soc. 1967
2. Howie, J.M., Fundamentals of semigroup theory, Oxford Univ. Press, 1995
3. Lawson, M.V., Inverse Semigroups: the theory of partial symmetries, World Scientific, 1998.
4. Petrich, M., Inverse semigroups, Willey, 1984
5. Petrich, M. and Reilly, N.R., Completely regular semigroups, Willey, 1999
Teaching method
Classes consist of oral explanation of the theory and of solving problems.
If the number of students is less than 5, classes will be tutorial. The student prepares the contents of each chapter using the specific bibliography indicated and solves related problems.