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200 10$aNumerical Semigroups and Applications /$fby Abdallah Assi, Pedro A. García-Sánchez
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (113 p.)
225 1 $aRSME Springer Series,$x2509-8896 ;$v1
300   $aDescription based upon print version of record.
311   $a3-319-41329-5 
320   $aIncludes bibliographical references and index.
327   $a1 Numerical semigroups, the basics -- 2 Irreducible numerical semigroups -- 3 Semigroup of an irreducible meromorphic series -- 4 Minimal presentations -- 5 Factorizations and divisibility.
330   $aThis work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. The focus is in particular on free semigroups, which are irreducible; semigroups associated with planar curves are of this kind. The authors also introduce semigroups associated with irreducible meromorphic series, and show how these are used in order to present the properties of planar curves. Invariants of non-unique factorizations for numerical semigroups are also studied. These invariants are computationally accessible in this setting, and thus this monograph can be used as an introduction to Factorization Theory. Since factorizations and divisibility are strongly connected, the authors show some applications to AG Codes in the final section. The book will be of value for undergraduate students (especially those at a higher level) and also for researchers wishing to focus on the state of art in numerical semigroups research.
410  0$aRSME Springer Series,$x2509-8896 ;$v1
606   $aGeometry, Algebraic
606   $aCommutative algebra
606   $aCommutative rings
606   $aAlgorithms
606   $aDiscrete mathematics
606   $aComputer science$xMathematics
606   $aAlgebraic Geometry
606   $aCommutative Rings and Algebras
606   $aAlgorithms
606   $aDiscrete Mathematics
606   $aDiscrete Mathematics in Computer Science
615  0$aGeometry, Algebraic.
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aAlgorithms.
615  0$aDiscrete mathematics.
615  0$aComputer science$xMathematics.
615 14$aAlgebraic Geometry.
615 24$aCommutative Rings and Algebras.
615 24$aAlgorithms.
615 24$aDiscrete Mathematics.
615 24$aDiscrete Mathematics in Computer Science.
676   $a510
700   $aAssi$b Abdallah$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756018
702   $aGarcía-Sánchez$b Pedro A$4aut$4http://id.loc.gov/vocabulary/relators/aut
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