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Numerical Semigroups and Applications

  • Abdallah Assi
  • Pedro A. García-Sánchez

Part of the RSME Springer Series book series (RSME, volume 1)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Abdallah Assi, Pedro A. García-Sánchez
    Pages 1-15
  3. Abdallah Assi, Pedro A. García-Sánchez
    Pages 17-29
  4. Abdallah Assi, Pedro A. García-Sánchez
    Pages 31-68
  5. Abdallah Assi, Pedro A. García-Sánchez
    Pages 69-83
  6. Abdallah Assi, Pedro A. García-Sánchez
    Pages 85-99
  7. Back Matter
    Pages 101-106

About this book

Introduction

This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. The focus is in particular on free semigroups, which are irreducible; semigroups associated with planar curves are of this kind. The authors also introduce semigroups associated with irreducible meromorphic series, and show how these are used in order to present the properties of planar curves. Invariants of non-unique factorizations for numerical semigroups are also studied. These invariants are computationally accessible in this setting, and thus this monograph can be used as an introduction to Factorization Theory. Since factorizations and divisibility are strongly connected, the authors show some applications to AG Codes in the final section. The book will be of value for undergraduate students (especially those at a higher level) and also for researchers wishing to focus on the state of art in numerical semigroups research.

Keywords

Numerical semigroup Algebraic curve AG codes Nonunique factorization invariants Combinatorics

Authors and affiliations

  • Abdallah Assi
    • 1
  • Pedro A. García-Sánchez
    • 2
  1. 1.Dèpartement de MathématiquesUniversité d'AngersAngersFrance
  2. 2.Departamento de ÁlgebraUniversidad de GranadaGranadaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-41330-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-41329-7
  • Online ISBN 978-3-319-41330-3
  • Series Print ISSN 2509-8888
  • Series Online ISSN 2509-8896
  • Buy this book on publisher's site