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＜電子ブック＞
Numerical Semigroups / by J.C. Rosales, P. A. García-Sánchez
(Developments in Mathematics. ISSN:2197795X ; 20)

版	1st ed. 2009.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	IX, 181 p. 7 illus : online resource
著者標目	*Rosales, J.C author García-Sánchez, P. A author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Group theory LCSH:Number theory LCSH:Universal algebra FREE:Algebra FREE:Group Theory and Generalizations FREE:Number Theory FREE:General Algebraic Systems FREE:Order, Lattices, Ordered Algebraic Structures
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-1-4419-0160-6

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