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Numerical semigroups and applications

Assi, Abdallah.

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Numerical semigroups and applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical semigroups and applications/ by Abdallah Assi, Pedro A. Garcia-Sanchez.
Author:	Assi, Abdallah.
other author:	Garcia-Sanchez, Pedro A.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xiv, 106 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Numerical semigroups, the basics -- 2 Irreducible numerical semigroups -- 3 Semigroup of an irreducible meromorphic series -- 4 Minimal presentations -- 5 Factorizations and divisibility.
Contained By:	Springer eBooks
Subject:	Semigroups. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-41330-3
ISBN:	9783319413303

Numerical semigroups and applications
Assi, Abdallah.

Numerical semigroups and applications[electronic resource] /by Abdallah Assi, Pedro A. Garcia-Sanchez. - Cham :Springer International Publishing :2016. - xiv, 106 p. :ill., digital ;24 cm. - RSME Springer series,v.12509-8888 ;. - RSME Springer series ;v.1..

1 Numerical semigroups, the basics -- 2 Irreducible numerical semigroups -- 3 Semigroup of an irreducible meromorphic series -- 4 Minimal presentations -- 5 Factorizations and divisibility.

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.

ISBN: 9783319413303

Standard No.: 10.1007/978-3-319-41330-3doiSubjects--Topical Terms:

609931
Semigroups.

LC Class. No.: QA182

Dewey Class. No.: 512

Numerical semigroups and applications
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100 1 $a Assi, Abdallah. $3 2210370
245 1 0 $a Numerical semigroups and applications $h [electronic resource] / $c by Abdallah Assi, Pedro A. Garcia-Sanchez.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a xiv, 106 p. : $b ill., digital ; $c 24 cm.
490 1 $a RSME Springer series, $x 2509-8888 ; $v v.1
505 0 $a 1 Numerical semigroups, the basics -- 2 Irreducible numerical semigroups -- 3 Semigroup of an irreducible meromorphic series -- 4 Minimal presentations -- 5 Factorizations and divisibility.
520 $a 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.
650 0 $a Semigroups. $3 609931
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Algebraic Geometry. $3 893861
650 2 4 $a Commutative Rings and Algebras. $3 891076
650 2 4 $a Algorithms. $3 536374
650 2 4 $a Combinatorics. $3 895617
650 2 4 $a Discrete Mathematics in Computer Science. $3 892513
700 1 $a Garcia-Sanchez, Pedro A. $3 2210371
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a RSME Springer series ; $v v.1. $3 2210372
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-41330-3
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