The Resource Numerical semigroups and applications, Abdallah Assi, Pedro A. García-Sánchez

Numerical semigroups and applications, Abdallah Assi, Pedro A. García-Sánchez

Label
Numerical semigroups and applications
Title
Numerical semigroups and applications
Statement of responsibility
Abdallah Assi, Pedro A. García-Sánchez
Creator
Contributor
Author
Subject
Genre
Language
eng
Summary
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
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Assi, Abdallah
Dewey number
512
Index
index present
LC call number
QA182
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
García-Sánchez, P. A.
Series statement
RSME Springer series
Series volume
volume 1
http://library.link/vocab/subjectName
  • Semigroups
  • MATHEMATICS
  • Semigroups
  • Algebra
  • Numerical analysis
  • Combinatorics & graph theory
  • Discrete mathematics
  • Algebraic geometry
Label
Numerical semigroups and applications, Abdallah Assi, Pedro A. García-Sánchez
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-41330-3
Instantiates
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Acknowledgments; Contents; 1 Numerical Semigroups, the Basics; 1.1 Notable Elements; 1.2 Numerical Semigroups with Maximal Embedding Dimension; 1.3 Special Gaps and Unitary Extensions of a Numerical Semigroup; 2 Irreducible Numerical Semigroups; 2.1 Characterizations of Irreducible Numerical Semigroups; 2.2 Decomposition of a Numerical Semigroup into Irreducible Semigroups; 2.3 Free Numerical Semigroups; 3 Semigroup of an Irreducible Meromorphic Series; 3.1 Some Notation; 3.2 Characteristic Sequences; 3.3 Contact; 3.4 The Local Case
  • 3.5 The Case of Curves with One Place at Infinity; 4 Minimal Presentations; 4.1 Generators and Relations; 4.2 Free Numerical Semigroups; 4.3 Graphs of Factorizations and Minimal Presentations; 4.4 Presentations and Binomial Ideals; 4.5 Shaded Sets and Generating Functions; 5 Factorizations and Divisibility; 5.1 Length-Based Invariants; 5.2 Distance-Based Invariants; 5.3 How Far Is an Irreducible from Being Prime; 5.4 Divisors and Feng -- Rao Distances; References; Index
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319413303
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)957464926
  • (OCoLC)ocn957464926
Label
Numerical semigroups and applications, Abdallah Assi, Pedro A. García-Sánchez
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-41330-3
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Acknowledgments; Contents; 1 Numerical Semigroups, the Basics; 1.1 Notable Elements; 1.2 Numerical Semigroups with Maximal Embedding Dimension; 1.3 Special Gaps and Unitary Extensions of a Numerical Semigroup; 2 Irreducible Numerical Semigroups; 2.1 Characterizations of Irreducible Numerical Semigroups; 2.2 Decomposition of a Numerical Semigroup into Irreducible Semigroups; 2.3 Free Numerical Semigroups; 3 Semigroup of an Irreducible Meromorphic Series; 3.1 Some Notation; 3.2 Characteristic Sequences; 3.3 Contact; 3.4 The Local Case
  • 3.5 The Case of Curves with One Place at Infinity; 4 Minimal Presentations; 4.1 Generators and Relations; 4.2 Free Numerical Semigroups; 4.3 Graphs of Factorizations and Minimal Presentations; 4.4 Presentations and Binomial Ideals; 4.5 Shaded Sets and Generating Functions; 5 Factorizations and Divisibility; 5.1 Length-Based Invariants; 5.2 Distance-Based Invariants; 5.3 How Far Is an Irreducible from Being Prime; 5.4 Divisors and Feng -- Rao Distances; References; Index
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319413303
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)957464926
  • (OCoLC)ocn957464926

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