Description
“Numerical Semigroups” is the first monograph devoted exclusively to the development of the theory of numerical semigroups. This concise, self-contained text is accessible to first year graduate students, giving the full background needed for readers unfamiliar with the topic. Researchers will find the tools presented useful in producing examples and counterexamples in other fields such as algebraic geometry, number theory, and linear programming. Introduction.- 1. Notable Elements.- 2. Numerical Semigroups with Maximal Embedding Dimension.- 3. Irreducible Numerical Semigropus.- 4. Proportionally Modular Numerical Semigroups.- 5. The Quotient of a Numerical Semigroup by a Positive Integer.- 6. Families of Numerical Semigroups Closed Under Finite Intersections and Adjoin of the Frobenius Number.- 7. Presentations of a Numerical Semigroup.- 8. The Gluing of Numerical Semigroups.- 9. Numerical Semigroups with Embedding Dimension Three.- 10. The Structure of a Numerical Semigroup.- Bibliography.- List of Symbols.- Index.
