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Numerical semigroups and applications

Assi, Abdallah.

Numerical semigroups and applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical semigroups and applicationsby 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.
Contained By:	Springer eBooks
Subject:	Semigroups.
Online resource:	http://dx.doi.org/10.1007/978-3-319-41330-3
ISBN:	9783319413303$q(electronic bk.)

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$q(electronic bk.)

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

239334
Semigroups.

LC Class. No.: QA182

Dewey Class. No.: 512

Numerical semigroups and applications
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245 1 0 $a Numerical semigroups and applications $h [electronic resource] / $c by Abdallah Assi, Pedro A. Garcia-Sanchez.
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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.
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650 1 4 $a Mathematics. $3 184409
650 2 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Commutative Rings and Algebras. $3 274057
650 2 4 $a Algorithms. $3 184661
650 2 4 $a Combinatorics. $3 274788
650 2 4 $a Discrete Mathematics in Computer Science. $3 274791
700 1 $a Garcia-Sanchez, Pedro A. $3 758705
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