Numerical Semigroups and Applications (RSME Springer Series, Band 1) - Softcover

Buch 1 von 5: RSME Springer

Assi, Abdallah

 
9783319823256: Numerical Semigroups and Applications (RSME Springer Series, Band 1)
Softcover
ISBN 10: 3319823256 ISBN 13: 9783319823256
Verlag: Springer, 2018

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

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.


Von der hinteren Coverseite

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.

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Verlag
Springer
Erscheinungsdatum
2018
Sprache
Englisch
ISBN 10 
3319823256
ISBN 13 
9783319823256
Einband
Taschenbuch
Anzahl der Seiten
120
Kontakt zum Hersteller
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Deutschland

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Hardcover