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Numerical Semigroups and Applications

Author: Abdallah Assi

Publisher: Springer Nature

Published: 2020-10-01

Total Pages: 138

ISBN-13: 3030549437

This book is an extended and revised version of "Numerical Semigroups with Applications," published by Springer as part of the RSME series. Like the first edition, it presents applications of numerical semigroups in Algebraic Geometry, Number Theory and Coding Theory. It starts by discussing the basic notions related to numerical semigroups and those needed to understand semigroups associated with irreducible meromorphic series. It then derives a series of applications in curves and factorization invariants. A new chapter is included, which offers a detailed review of ideals for numerical semigroups. Based on this new chapter, descriptions of the module of Kähler differentials for an algebroid curve and for a polynomial curve are provided. Moreover, the concept of tame degree has been included, and is viewed in relation to other factorization invariants appearing in the first edition. This content highlights new applications of numerical semigroups and their ideals, following in the spirit of the first edition.

Numerical Semigroups

Author: J.C. Rosales

Publisher: Springer Science & Business Media

Published: 2009-12-24

Total Pages: 186

ISBN-13: 1441901604

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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.

Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains

Author: Valentina Barucci

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 95

ISBN-13: 0821805444

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In Chapter I, various (numerical) semigroup-theoretic concepts and constructions are introduced and characterized. Applications in Chapter II are made to the study of Noetherian local one-dimensional analytically irreducible integral domains, especially for the Gorenstein, maximal embedding dimension, and Arf cases, as well as to the so-called Kunz case, a pervasive kind of domain of Cohen-Macaulay type 2.

Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains

Author: Valentina Barucci

Publisher:

Published: 1997

Total Pages: 78

ISBN-13: 9781470401832

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Numerical Semigroups

Author: Valentina Barucci

Publisher: Springer Nature

Published: 2020-05-13

Total Pages: 373

ISBN-13: 3030408221

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This book presents the state of the art on numerical semigroups and related subjects, offering different perspectives on research in the field and including results and examples that are very difficult to find in a structured exposition elsewhere. The contents comprise the proceedings of the 2018 INdAM “International Meeting on Numerical Semigroups”, held in Cortona, Italy. Talks at the meeting centered not only on traditional types of numerical semigroups, such as Arf or symmetric, and their usual properties, but also on related types of semigroups, such as affine, Puiseux, Weierstrass, and primary, and their applications in other branches of algebra, including semigroup rings, coding theory, star operations, and Hilbert functions. The papers in the book reflect the variety of the talks and derive from research areas including Semigroup Theory, Factorization Theory, Algebraic Geometry, Combinatorics, Commutative Algebra, Coding Theory, and Number Theory. The book is intended for researchers and students who want to learn about recent developments in the theory of numerical semigroups and its connections with other research fields.

Algebraic Geometry Modeling in Information Theory

Author: Edgar Martinez-Moro

Publisher: World Scientific

Published: 2013

Total Pages: 334

ISBN-13: 9814335762

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Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.

Semigroups And Applications

Author: John M Howie

Publisher: World Scientific

Published: 1998-12-08

Total Pages: 290

ISBN-13: 9814545430

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This volume contains contributions from leading experts in the rapidly developing field of semigroup theory. The subject, now some 60 years old, began by imitating group theory and ring theory, but quickly developed an impetus of its own, and the semigroup turned out to be the most useful algebraic object in theoretical computer science.

Quantum Dynamical Semigroups and Applications

Author: Robert Alicki

Publisher: Springer Science & Business Media

Published: 2007-04-23

Total Pages: 138

ISBN-13: 354070860X

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Reinvigorated by advances and insights the quantum theory of irreversible processes has recently attracted growing attention. This volume introduces the very basic concepts of semigroup dynamics of open quantum systems and reviews a variety of modern applications. Originally published as Volume 286 (1987) in Lecture in Physics, this volume has been newly typeset, revised and corrected and also expanded to include a review on recent developments.

A Project-Based Guide to Undergraduate Research in Mathematics

Author: Pamela E. Harris

Publisher: Springer Nature

Published: 2020-04-17

Total Pages: 324

ISBN-13: 3030378535

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This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs. The chapters in this work span a variety of topical areas of pure and applied mathematics and mathematics education. Each chapter gives a self-contained introduction on a research topic with an emphasis on the specific tools and knowledge needed to create and maintain fruitful research programs for undergraduates. Some of the topics discussed include:• Disease modeling• Tropical curves and surfaces• Numerical semigroups• Mathematics EducationThis volume will primarily appeal to undergraduate students interested in pursuing research projects and faculty members seeking to mentor them. It may also aid students and faculty participating in independent studies and capstone projects.

Commutative Algebra and Its Applications

Author: Marco Fontana

Publisher: Walter de Gruyter

Published: 2009

Total Pages: 395

ISBN-13: 311020746X

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This volume contains selected refereed papers based on lectures presented at the 'Fifth International Fez Conference on Commutative Algebra and Applications' that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.