Overview
- First monograph devoted exclusively to the study of numerical semigroups
- Presents various applications of numerical semigroups including number theory, coding theory, algebraic geometry, and others
- The text is self contained
- Presents content ranging from the basics to open research problems
- Accessible to any first year graduate student
- Includes exercises that invite the reader to prove results published in recent mathematical journals
- Includes supplementary material: sn.pub/extras
Part of the book series: Developments in Mathematics (DEVM, volume 20)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Reviews
From the reviews:
“This book is a monograph, a summary of papers written on a … specialized subject. … In the body of the book, each topic … is accompanied by explanations as to which reference they appear in. … the writing is extremely clear, and the ideas well motivated. … The exercises at the end of the chapters are well taken … . without boring the reader or becoming too lengthy, the book does a very impressive job of being self-contained, and friendly to readers and students.” (Marion Cohen, The Mathematical Association of America, June, 2010)
“It is not often you can read a book in mathematics without a lot of background knowledge, and still reach the front of research of the subject. This is in fact possible with this book. … The exercises after all chapters help the reader to understand the concepts, and some of them also extend the subject by introducing new concepts. … all basic concepts are introduced in a purely elementary way, and to understand this book, one needs no background in algebraic geometry.” (Ralf Froberg, Semigroup Forum, Vol. 81, 2010)
“This book presents the theory of numerical semigroups, the development of which essentially is due to the two authors. They collected and proved all the results obtained so far in a very clear and self-contained way. Hence the text will be of interest for everyone working in the above mentioned fields and for everybody interested in the set of natural numbers, the understanding of which is heavily supported by the abstract theory of semigroups … .” (H. Mitsch, Monatshefte für Mathematik, Vol. 161 (1), August, 2010)
“This book gives a very readable account … that should be more widely known and will be useful to both researchers in the area and students new to the subject. … The exposition in the book is very good and can be followed even by talented undergraduates. … It is enjoyable and easy to read and serves as both a goodway to learn a new subject for those who do not know much about the area, and a very useful research reference for experts.” (Nathan Kaplan, Zentralblatt MATH, Vol. 1220, 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Numerical Semigroups
Authors: J.C. Rosales, P. A. García-Sánchez
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-1-4419-0160-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2009
Hardcover ISBN: 978-1-4419-0159-0Published: 28 September 2009
Softcover ISBN: 978-1-4614-2456-7Published: 03 March 2012
eBook ISBN: 978-1-4419-0160-6Published: 24 December 2009
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: IX, 181
Number of Illustrations: 7 b/w illustrations
Topics: Algebra, Group Theory and Generalizations, Number Theory, General Algebraic Systems, Order, Lattices, Ordered Algebraic Structures