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Author Assi, Abdallah,
Title Numerical semigroups and applications / Abdallah Assi, Pedro A. Garcia-Sanchez.
Imprint Switzerland : Springer, 2016.

LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
View online
Author Assi, Abdallah,
Series RSME Springer series ; volume 1
RSME Springer series ; v. 1.
Subject Semigroups.
Alt Name Garcia-Sanchez, P. A.,
LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
View online
Author Assi, Abdallah,
Series RSME Springer series ; volume 1
RSME Springer series ; v. 1.
Subject Semigroups.
Genre/Form Electronic books.
Alt Name Garcia-Sanchez, P. A.,
Description 1 online resource.
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.
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.
Access License restrictions may limit access.
Note Online resource; title from PDF title page (EBSCO, viewed September 1, 2016).
ISBN 9783319413303 (electronic bk.)
3319413309 (electronic bk.)
9783319413297
3319413295
OCLC # 957464926
Additional Format Print version: Assi, Abdallah. Numerical semigroups and applications. 9783319413297 3319413295 (OCoLC)951761231