Multiplicative Ideal Theory And Factorization Theory

Author : Scott Chapman,Marco Fontana,Alfred Geroldinger,Bruce Olberding
Publisher : Springer
Page : 407 pages
File Size : 43,8 Mb
Release : 2016-07-29
Category : Mathematics
ISBN : 9783319388557

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Multiplicative Ideal Theory and Factorization Theory by Scott Chapman,Marco Fontana,Alfred Geroldinger,Bruce Olberding Pdf

This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.

Author : Robert W. Gilmer
Publisher : New York : M. Dekker
Page : 632 pages
File Size : 52,7 Mb
Release : 1972
Category : Mathematics
ISBN : UVA:X001320691

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Multiplicative Ideal Theory by Robert W. Gilmer Pdf

Author : Franz Halter-Koch
Publisher : CRC Press
Page : 444 pages
File Size : 49,8 Mb
Release : 1998-04-21
Category : Mathematics
ISBN : 0824701860

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Ideal Systems by Franz Halter-Koch Pdf

"Provides for the first time a concise introduction to general and multiplicative ideal theory, valid for commutative rings and monoids and presented in the language of ideal systems on (commutative) monoids."

Author : Anonim
Publisher : Academic Press
Page : 297 pages
File Size : 55,5 Mb
Release : 1971-10-11
Category : Mathematics
ISBN : 0080873561

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Multiplicative Theory of Ideals by Anonim Pdf

Multiplicative Theory of Ideals

Author : Robert W. Gilmer
Publisher : Unknown
Page : 700 pages
File Size : 44,9 Mb
Release : 1968
Category : Ideals (Algebra)
ISBN : LCCN:76384764

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Multiplicative Ideal Theory by Robert W. Gilmer Pdf

Author : James W. Brewer,Sarah Glaz,William Heinzer,Bruce Olberding
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 42,6 Mb
Release : 2006-12-15
Category : Mathematics
ISBN : 9780387367170

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Multiplicative Ideal Theory in Commutative Algebra by James W. Brewer,Sarah Glaz,William Heinzer,Bruce Olberding Pdf

This volume, a tribute to the work of Robert Gilmer, consists of twenty-four articles authored by his most prominent students and followers. These articles combine surveys of past work by Gilmer and others, recent results which have never before seen print, open problems, and extensive bibliographies. The entire collection provides an in-depth overview of the topics of research in a significant and large area of commutative algebra.

Author : Alberto Facchini,Marco Fontana,Alfred Geroldinger,Bruce Olberding
Publisher : Springer Nature
Page : 341 pages
File Size : 48,5 Mb
Release : 2020-06-02
Category : Mathematics
ISBN : 9783030434168

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Advances in Rings, Modules and Factorizations by Alberto Facchini,Marco Fontana,Alfred Geroldinger,Bruce Olberding Pdf

Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra. A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches.

Author : David J. Grynkiewicz
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 49,7 Mb
Release : 2013-05-30
Category : Mathematics
ISBN : 9783319004167

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Structural Additive Theory by David J. Grynkiewicz Pdf

​Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.

Author : David J. Grynkiewicz
Publisher : Springer Nature
Page : 291 pages
File Size : 41,6 Mb
Release : 2022-10-26
Category : Mathematics
ISBN : 9783031148699

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The Characterization of Finite Elasticities by David J. Grynkiewicz Pdf

This book develops a new theory in convex geometry, generalizing positive bases and related to Carathéordory’s Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra) This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization. While factorization into irreducibles, called atoms, generally fails to be unique, there are various measures of how badly this can fail. Among the most important is the elasticity, which measures the ratio between the maximum and minimum number of atoms in any factorization. Having finite elasticity is a key indicator that factorization, while not unique, is not completely wild. Via the developed material in convex geometry, we characterize when finite elasticity holds for any Krull domain with finitely generated class group $G$, with the results extending more generally to transfer Krull monoids. This book is aimed at researchers in the field but is written to also be accessible for graduate students and general mathematicians.

Author : Melvyn B. Nathanson
Publisher : Springer Nature
Page : 445 pages
File Size : 52,6 Mb
Release : 2021-08-12
Category : Mathematics
ISBN : 9783030679965

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

This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America, Europe, and Asia. The 2020 Zoom conference was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain 25 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003 at the CUNY Graduate Center, the workshop surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, zero-sum sequences, minimal complements, analytic and prime number theory, Hausdorff dimension, combinatorial and discrete geometry, and Ramsey theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

Author : Abdallah Assi,Marco D'Anna,Pedro A. García-Sánchez
Publisher : Springer Nature
Page : 138 pages
File Size : 44,9 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 : Heather A. Harrington,Mohamed Omar,Matthew Wright
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 50,6 Mb
Release : 2017-03-16
Category : Commutative algebra -- Computational aspects and applications -- Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
ISBN : 9781470423216

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Algebraic and Geometric Methods in Discrete Mathematics by Heather A. Harrington,Mohamed Omar,Matthew Wright Pdf

This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas. The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics. Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks. This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.

Author : Scott T. Chapman
Publisher : CRC Press
Page : 410 pages
File Size : 43,8 Mb
Release : 2005-03-01
Category : Mathematics
ISBN : 9781420028249

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Arithmetical Properties of Commutative Rings and Monoids by Scott T. Chapman Pdf

The study of nonunique factorizations of elements into irreducible elements in commutative rings and monoids has emerged as an independent area of research only over the last 30 years and has enjoyed a recent flurry of activity and advancement. This book presents the proceedings of two recent meetings that gathered key researchers from around the w

Author : Ayman Badawi,Jim Coykendall
Publisher : Springer Nature
Page : 317 pages
File Size : 40,9 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.

Author : David Dobbs
Publisher : CRC Press
Page : 578 pages
File Size : 45,7 Mb
Release : 2023-08-25
Category : Mathematics
ISBN : 9781000939637

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Advances in Commutative Ring Theory by David Dobbs Pdf

"Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."