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Numerical Semigroups [electronic resource] /by J.C. Rosales, P. A. García-Sánchez.

by Rosales, J.C [author.]; García-Sánchez, P. A [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Developments in Mathematics, Diophantine Approximation: Festschrift for Wolfgang Schmidt: 20Publisher: New York, NY : Springer New York, 2009.Edition: First.Description: IX, 181p. 7 illus. online resource.ISBN: 9781441901606.Subject(s): Mathematics | Algebra | Group theory | Number theory | Mathematics | Group Theory and Generalizations | General Algebraic Systems | Order, Lattices, Ordered Algebraic Structures | Number TheoryDDC classification: 512.2 Online resources: Click here to access online
Contents:
Notable elements -- Numerical semigroups with maximal embedding dimension -- Irreducible numerical semigroups -- Proportionally modular numerical semigroups -- The quotient of a numerical semigroup by a positive integer -- Families of numerical semigroups closed under finite intersections and adjoin of the Frobenius number -- Presentations of a numerical semigroup -- The gluing of numerical semigroups -- Numerical semigroups with embedding dimension three -- The structure of a numerical semigroup.
In: Springer eBooksSummary: This monograph is the first devoted exclusively to the development of the theory of numerical semigroups. In this concise, self-contained text, graduate students and researchers will benefit from this broad exposition of the topic. Key features of "Numerical Semigroups" include: - Content ranging from the basics to open research problems and the latest advances in the field; - Exercises at the end of each chapter that expand upon and support the material; - Emphasis on the computational aspects of the theory; algorithms are presented to provide effective calculations; - Many examples that illustrate the concepts and algorithms; - Presentation of various connections between numerical semigroups and number theory, coding theory, algebraic geometry, linear programming, and commutative algebra would be of significant interest to researchers. "Numerical Semigroups" is accessible to first year graduate students, with only a basic knowledge of algebra required, giving the full background needed for readers not familiar with the topic. Researchers will find the tools presented useful in producing examples and counterexamples in other fields such as algebraic geometry, number theory, and linear programming.
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Notable elements -- Numerical semigroups with maximal embedding dimension -- Irreducible numerical semigroups -- Proportionally modular numerical semigroups -- The quotient of a numerical semigroup by a positive integer -- Families of numerical semigroups closed under finite intersections and adjoin of the Frobenius number -- Presentations of a numerical semigroup -- The gluing of numerical semigroups -- Numerical semigroups with embedding dimension three -- The structure of a numerical semigroup.

This monograph is the first devoted exclusively to the development of the theory of numerical semigroups. In this concise, self-contained text, graduate students and researchers will benefit from this broad exposition of the topic. Key features of "Numerical Semigroups" include: - Content ranging from the basics to open research problems and the latest advances in the field; - Exercises at the end of each chapter that expand upon and support the material; - Emphasis on the computational aspects of the theory; algorithms are presented to provide effective calculations; - Many examples that illustrate the concepts and algorithms; - Presentation of various connections between numerical semigroups and number theory, coding theory, algebraic geometry, linear programming, and commutative algebra would be of significant interest to researchers. "Numerical Semigroups" is accessible to first year graduate students, with only a basic knowledge of algebra required, giving the full background needed for readers not familiar with the topic. Researchers will find the tools presented useful in producing examples and counterexamples in other fields such as algebraic geometry, number theory, and linear programming.

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