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RSME Springer Series

Numerical Semigroups and Applications

Authors: Assi, Abdallah, García-Sánchez, Pedro A.

  • Useful for any undergraduate student, and also for researchers wishing to focus on the state of art in numerical semigroups research
  • Contains many examples and tutorials with the (free) numericalsgps GAP package
  • Shows the ubiquity of numerical semigroups
see more benefits

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-41330-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-3-319-41329-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

Abdallah Assi graduated in Mathematics at the University Joseph Fourier (Grenoble, France). He obtained his Ph.D. in Mathematics at the same university and his HDR-Habilitation à diriger les recherches- at the University of Angers (France). He has a parmanent position at the Department of Mathematics in the University of Angers since 1995. His research interests are in affine geometry, numerical semigroups, and the theory of singularities.

Pedro A. Garcia-Sanchez was born in Granada, Spain, in 1969. Since 1992 he teaches in the Departmento de Algebra at the Universidad de Granada. He graduated in Mathematics and in Computer Science (Diploma) in 1992. He defended his PhD Thesis "Affine semigroups" in 1996, and since 1999 he has a permanent position at the Universidad de Granada. His main research interests are numerical semigroups, commutative monoids and nonunique factorization invariants.


Table of contents (5 chapters)

  • Numerical Semigroups, the Basics

    Assi, Abdallah (et al.)

    Pages 1-15

  • Irreducible Numerical Semigroups

    Assi, Abdallah (et al.)

    Pages 17-29

  • Semigroup of an Irreducible Meromorphic Series

    Assi, Abdallah (et al.)

    Pages 31-68

  • Minimal Presentations

    Assi, Abdallah (et al.)

    Pages 69-83

  • Factorizations and Divisibility

    Assi, Abdallah (et al.)

    Pages 85-99

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-41330-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-3-319-41329-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Semigroups and Applications
Authors
Series Title
RSME Springer Series
Series Volume
1
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-41330-3
DOI
10.1007/978-3-319-41330-3
Hardcover ISBN
978-3-319-41329-7
Series ISSN
2509-8888
Edition Number
1
Number of Pages
XIV, 106
Number of Illustrations and Tables
5 b/w illustrations
Topics