Numerical Semigroups

  • J.C. Rosales
  • P. A. García-Sánchez
Part of the Developments in Mathematics book series (DEVM, volume 20)

Table of contents

  1. Front Matter
    Pages i-ix
  2. J.C. Rosales, P.A. García-Sánchez
    Pages 1-3
  3. J.C. Rosales, P.A. García-Sánchez
    Pages 5-18
  4. J.C. Rosales, P.A. García-Sánchez
    Pages 19-32
  5. J.C. Rosales, P.A. García-Sánchez
    Pages 33-55
  6. J.C. Rosales, P.A. García-Sánchez
    Pages 57-76
  7. J.C. Rosales, P.A. García-Sánchez
    Pages 77-90
  8. J.C. Rosales, P.A. García-Sánchez
    Pages 105-122
  9. J.C. Rosales, P.A. García-Sánchez
    Pages 123-136
  10. J.C. Rosales, P.A. García-Sánchez
    Pages 137-154
  11. J.C. Rosales, P.A. García-Sánchez
    Pages 155-169
  12. Back Matter
    Pages 171-181

About this book

Introduction

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.

Keywords

Additive Semigroups Embedding Dimension Frobenius Number Group theory Irreducible Modular Monoid Number theory Numerical Semigroups coding theory

Authors and affiliations

  • J.C. Rosales
    • 1
  • P. A. García-Sánchez
    • 2
  1. 1.Faculty of Sciences, Department of AlgebraUniversity of GranadaGranadaSpain
  2. 2.Faculty of Sciences, Department of AlgebraUniversity of GranadaGranadaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-0160-6
  • Copyright Information Springer Science+Business Media, LLC 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-0159-0
  • Online ISBN 978-1-4419-0160-6
  • Series Print ISSN 1389-2177