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"Numerical Semigroups" is the first monograph devoted exclusively to the development of the theory of numerical semigroups. This concise, self-contained text is accessible to first year graduate students, giving the full background needed for readers unfamiliar 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.…mehr
"Numerical Semigroups" is the first monograph devoted exclusively to the development of the theory of numerical semigroups. This concise, self-contained text is accessible to first year graduate students, giving the full background needed for readers unfamiliar 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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Introduction.-1. Notable Elements.-2. Numerical Semigroups with Maximal Embedding Dimension.-3. Irreducible Numerical Semigropus.-4. Proportionally Modular Numerical Semigroups.-5. The Quotient of a Numerical Semigroup by a Positive Integer.-6. Families of Numerical Semigroups Closed Under Finite Intersections and Adjoin of the Frobenius Number.-7. Presentations of a Numerical Semigroup.-8. The Gluing of Numerical Semigroups.-9. Numerical Semigroups with Embedding Dimension Three.-10. The Structure of a Numerical Semigroup.-Bibliography.-List of Symbols.-Index.
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)…mehr
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