Numerical Semigroups And Applications

Author : Abdallah Assi,Marco D'Anna,Pedro A. García-Sánchez
Publisher : Springer Nature
Page : 138 pages
File Size : 43,6 Mb
Release : 2020-10-01
Category : Mathematics
ISBN : 9783030549435

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Numerical Semigroups and Applications by Abdallah Assi,Marco D'Anna,Pedro A. García-Sánchez Pdf

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.

Author : Valentina Barucci,David E. Dobbs,Marco Fontana
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 54,8 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805442

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Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains by Valentina Barucci,David E. Dobbs,Marco Fontana Pdf

If $k$ is a field, $T$ an analytic indeterminate over $k$, and $n_1, \ldots, n_h$ are natural numbers, then the semigroup ring $A = k[[T^{n_1}, \ldots, T^{n_h}]]$ is a Noetherian local one-dimensional domain whose integral closure, $k[[T]]$, is a finitely generated $A$-module. There is clearly a close connection between $A$ and the numerical semigroup generated by $n_1, \ldots, n_h$. More generally, let $A$ be a Noetherian local domain which is analytically irreducible and one-dimensional (equivalently, whose integral closure $V$ is a DVR and a finitely generated $A$-module). As noted by Kunz in 1970, some algebraic properties of $A$ such as ``Gorenstein'' can be characterized by using the numerical semigroup of $A$ (i.e., the subset of $N$ consisting of all the images of nonzero elements of $A$ under the valuation associated to $V$ ). This book's main purpose is to deepen the semigroup-theoretic approach in studying rings A of the above kind, thereby enlarging the class of applications well beyond semigroup rings. For this reason, Chapter I is devoted to introducing several new semigroup-theoretic properties which are analogous to various classical ring-theoretic concepts. Then, in Chapter II, the earlier material is applied in systematically studying rings $A$ of the above type. As the authors examine the connections between semigroup-theoretic properties and the correspondingly named ring-theoretic properties, there are some perfect characterizations (symmetric $\Leftrightarrow$ Gorenstein; pseudo-symmetric $\Leftrightarrow$ Kunz, a new class of domains of Cohen-Macaulay type 2). However, some of the semigroup properties (such as ``Arf'' and ``maximal embedding dimension'') do not, by themselves, characterize the corresponding ring properties. To forge such characterizations, one also needs to compare the semigroup- and ring-theoretic notions of ``type''. For this reason, the book introduces and extensively uses ``type sequences'' in both the semigroup and the ring contexts.

Author : J.C. Rosales,P. A. García-Sánchez
Publisher : Springer Science & Business Media
Page : 186 pages
File Size : 52,9 Mb
Release : 2009-12-24
Category : Mathematics
ISBN : 9781441901606

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Numerical Semigroups by J.C. Rosales,P. A. García-Sánchez Pdf

"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.

Author : Valentina Barucci,David E. Dobbs,Marco Fontana
Publisher : Unknown
Page : 78 pages
File Size : 45,5 Mb
Release : 1997
Category : Ideals
ISBN : 1470401835

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Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains by Valentina Barucci,David E. Dobbs,Marco Fontana Pdf

Author : Valentina Barucci,Scott Chapman,Marco D'Anna,Ralf Fröberg
Publisher : Springer Nature
Page : 373 pages
File Size : 45,5 Mb
Release : 2020-05-13
Category : Mathematics
ISBN : 9783030408220

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Numerical Semigroups by Valentina Barucci,Scott Chapman,Marco D'Anna,Ralf Fröberg Pdf

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.

Author : John M Howie,Nik Ruskuc
Publisher : World Scientific
Page : 290 pages
File Size : 45,5 Mb
Release : 1998-12-08
Category : Electronic
ISBN : 9789814545433

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Semigroups And Applications by John M Howie,Nik Ruskuc Pdf

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.

Author : John Rhodes
Publisher : #N/A
Page : 548 pages
File Size : 53,8 Mb
Release : 1991-03-06
Category : Electronic
ISBN : 9789814612715

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Monoids And Semigroups With Applications - Proceedings Of The Berkeley Workshop In Monoids by John Rhodes Pdf

The purpose of the Berkeley Workshop on Monoids was to give expository talks by the most qualified experts in the emerging main areas of monoid and semigroup theory including applications to theoretical computer science. This was supplemented with current research papers. The topics covered, in an accessible way for the mathematical and theoretical computer community, were: Kernels and expansions in semigroup theory; Implicit operations; Inverse monoids; Varieties of semigroups and universal algebra; Linear semigroups and monoids of Lie type; Monoids acting on tress; Synthesis theorem, regular semigroups, and applications; Type-II conjecture; Application to theoretical computer science and decision problems.

Author : Marco Fontana
Publisher : Walter de Gruyter
Page : 395 pages
File Size : 45,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9783110207460

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Commutative Algebra and Its Applications by Marco Fontana Pdf

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.

Author : Paul-Jean Cahen,Marco Fontana,Evan Houston,Salah-Eddine Kabbaj
Publisher : CRC Press
Page : 489 pages
File Size : 42,7 Mb
Release : 2023-06-14
Category : Mathematics
ISBN : 9781000946765

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Commutative Ring Theory by Paul-Jean Cahen,Marco Fontana,Evan Houston,Salah-Eddine Kabbaj Pdf

Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco. The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry.

Author : Robert Alicki,K. Lendi
Publisher : Springer Science & Business Media
Page : 138 pages
File Size : 43,8 Mb
Release : 2007-04-23
Category : Science
ISBN : 9783540708605

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Quantum Dynamical Semigroups and Applications by Robert Alicki,K. Lendi Pdf

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.

Author : Gerard Lallement
Publisher : John Wiley & Sons
Page : 404 pages
File Size : 52,9 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015014357902

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Semigroups and Combinatorial Applications by Gerard Lallement Pdf

The purpose of this book is to present those parts of the theory of semigroups that are directly related to automata theory, algebraic linguistics, and combinatorics. Publications in these mathematical disciplines contained methods and results pertaining to the algebraic theory of semigroups, and this has contributed to considerable enrichment of the theory, enlargement of its scope, and improved its potential to become a major domain of algebra. Semigroup theory appears to provide a general framework for unifying and clarifying a number of topics in fields that at first sight appear unrelated. This book is intended as a textbook for graduate students in mathematics and computer science, and as a reference book for researchers interested in associative structures.

Author : Viviana Ene,Ezra Miller
Publisher : Springer
Page : 167 pages
File Size : 53,5 Mb
Release : 2018-06-07
Category : Mathematics
ISBN : 9783319904931

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Multigraded Algebra and Applications by Viviana Ene,Ezra Miller Pdf

This volume contains research papers and surveys reflecting the topics discussed at the EMS Summer School on Multigraded Algebra and Applications held in Romania in August 2016. The school, which served as the 24th National School on Algebra, presented the main research directions of combinatorial commutative algebra with a strong focus on its applications in combinatorics, statistics, and biology. Recent progress in the field has led to new insights and suggested algebraic techniques for solving real-world data analysis problems. The summer school and resulting proceedings volume have raised numerous novel questions and encouraged a more interdisciplinary approach for young researchers when considering problems in pure and applied mathematical research. Featured topics in this volume include toric rings, binomial edge ideals, Betti numbers for numerical semigroup rings, and Waldschmidt constants. Researchers and graduate students interested in the developments of the field will find this book useful for their studies.

Author : Joaquim Borges,Mercè Villanueva
Publisher : Univ. Autònoma de Barcelona
Page : 289 pages
File Size : 48,6 Mb
Release : 2011-09-05
Category : Education
ISBN : 9788449026881

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3rd International Castle Meeting on Coding Theory and Applications by Joaquim Borges,Mercè Villanueva Pdf

In 1999, a conference called International Meeting on Coding Theory and Cryptography took place at Mota Castle in Castilia (Spain). The conference had great acceptance within the community of coding theory and cryptography researchers. At that moment, and also nowadays, there are not many international workshops about these topics, at least if we compare with other mathematical and engineering subjects of research. Therefore, the general desire was to continue with more Castle Meetings. However, the following conference did not take place until 2008. In that case, the conference was called II International Castle Meeting on Coding Theory and Applications allowing more topics related to coding theory apart from cryptography. Such conference took place at Mota Castle again and the number of participants was similar to the previous edition. The present edition of the conference, called III International Castle Meeting on Coding Theory and Applications has been held at Cardona Castle in Catalonia (Spain). The number of communications has increased and a number of selected papers will be published in a special issue of the journal Designs, Codes and Cryptography. As in the previous editions, the conference has been of high level with notorious invited speakers and scientic committee members.

Author : Melvyn B. Nathanson
Publisher : Springer Nature
Page : 290 pages
File Size : 45,6 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 9783031107962

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Combinatorial and Additive Number Theory V by Melvyn B. Nathanson Pdf

This proceedings volume, the fifth in a series from the Combinatorial and Additive Number Theory (CANT) conferences, is based on talks from the 19th annual workshop, held online due to the COVID-19 pandemic. Organized every year since 2003 by the New York Number Theory Seminar at the CUNY Graduate Center, the workshops survey state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. The CANT 2021 meeting featured over a hundred speakers from North and South America, Europe, Asia, Australia, and New Zealand, and was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain peer-reviewed and edited papers on current topics in number theory. Topics featured in this volume include sumsets, minimal bases, Sidon sets, analytic and prime number theory, combinatorial and discrete geometry, numerical semigroups, and a survey of expansion, divisibility, and parity. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

Author : Ayman Badawi,Jim Coykendall
Publisher : Springer Nature
Page : 317 pages
File Size : 47,9 Mb
Release : 2022-03-11
Category : Mathematics
ISBN : 9789811684227

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Rings, Monoids and Module Theory by Ayman Badawi,Jim Coykendall Pdf

This book contains select papers on rings, monoids and module theory which are presented at the 3rd International Conference on Mathematics and Statistics (AUS-ICMS 2020) held at the American University of Sharjah, United Arab Emirates, from 6–9 February 2020. This conference was held in honour of the work of the distinguished algebraist Daniel D. Anderson. Many participants and colleagues from around the world felt it appropriate to acknowledge his broad and sweeping contributions to research in algebra by writing an edited volume in his honor. The topics covered are, inevitably, a cross-section of the vast expansion of modern algebra. The book is divided into two sections—surveys and recent research developments—with each section hopefully offering symbiotic utility to the reader. The book contains a balanced mix of survey papers, which will enable expert and non-expert alike to get a good overview of developments across a range of areas of algebra. The book is expected to be of interest to both beginning graduate students and experienced researchers.