Numerical Semigroups
Code
9631
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
Objectives
Students should get familiar with numerical semigroup concepts.
Prerequisites
None.
Subject matter
1. Notable elements.
2. GAP package "numericalsgps".
3. Numerical semigroups with maximal embedding dimension.
4. Irreducible numerical semigroups.
5. Proportionally modular numerical semigroups.
6. The quotient of a numerical semigroup by a positive integer.
7. Presentations of a numerical semigroup.
Bibliography
1. Rosales, J.C. e García-Sánchez, P.A., Numerical Semigroups, Springer, 2009.
2. Rosales, J.C. e García-Sánchez, P.A., Finitely generated commutative monoids, Nova Science Publishers, New York, 1999.
3. Delgado, M., García-Sánchez, P.A. E Morais, J., “numericalsgps”: a GAP package on numerical semigroups.
(http://www.gap-system.org/Packages/numericalsgps.html).
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.
Evaluation method
Continuous evaluation and/or final essay/exam.