Numerical Semigroups

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This monograph is the first devoted exclusively to the development of the theory of numerical semigroups. In this concise, self-contained text, graduate students and researchers will benefit from this broad exposition of the topic.

Key features of "Numerical Semigroups" include:

- Content ranging from the basics to open research problems and the latest advances in the field;

- Exercises at the end of each chapter that expand upon and support the material;

- Emphasis on the computational aspects of the theory; algorithms are presented to provide effective calculations;

- Many examples that illustrate the concepts and algorithms;

- Presentation of various connections between numerical semigroups and number theory, coding theory, algebraic geometry, linear programming, and commutative algebra would be of significant interest to researchers.

"Numerical Semigroups" is accessible to first year graduate students, with only a basic knowledge of algebra required, giving the full background needed for readers not familiar 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.

Author(s): J.C. Rosales, P. A. García-Sánchez (auth.)
Series: Developments in Mathematics 20
Edition: 1
Publisher: Springer-Verlag New York
Year: 2009

Language: English
Pages: 181
Tags: Group Theory and Generalizations; General Algebraic Systems; Order, Lattices, Ordered Algebraic Structures; Number Theory

Front Matter....Pages i-ix
Introduction....Pages 1-3
Notable elements....Pages 5-18
Numerical semigroups with maximal embedding dimension....Pages 19-32
Irreducible numerical semigroups....Pages 33-55
Proportionally modular numerical semigroups....Pages 57-76
The quotient of a numerical semigroup by a positive integer....Pages 77-90
Families of numerical semigroups closed under finite intersections and adjoin of the Frobenius number....Pages 91-104
Presentations of a numerical semigroup....Pages 105-122
The gluing of numerical semigroups....Pages 123-136
Numerical semigroups with embedding dimension three....Pages 137-154
The structure of a numerical semigroup....Pages 155-169
Back Matter....Pages 171-181