Rings And Factorization

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Rings and Factorization

David William Sharpe
Rings and Factorization Book PDF

Author : David William Sharpe
Publisher : CUP Archive
Page : 132 pages
File Size : 44,5 Mb
Release : 1987-08-28
Category : Mathematics
ISBN : 0521337186

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Rings and Factorization by David William Sharpe Pdf

This textbook is an introduction to the concept of factorization and its application to problems in algebra and number theory. With the minimum of prerequisites, the reader is introduced to the notion of rings, fields, prime elements and unique factorization. The author shows how concepts can be applied to a variety of examples such as factorizing polynomials, finding determinants of matrices and Fermat's 'two-squares theorem'. Based on an undergraduate course given at the University of Sheffield, Dr Sharpe has included numerous examples which demonstrate how frequently these ideas are useful in concrete, rather than abstract, settings. The book also contains many exercises of varying degrees of difficulty together with hints and solutions. Second and third year undergraduates will find this a readable and enjoyable account of a subject lying at the heart of much of mathematics.

Advances in Rings, Modules and Factorizations

Alberto Facchini,Marco Fontana,Alfred Geroldinger,Bruce Olberding
Advances in Rings Modules and Factorizations Book PDF

Author : Alberto Facchini,Marco Fontana,Alfred Geroldinger,Bruce Olberding
Publisher : Springer Nature
Page : 341 pages
File Size : 46,5 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.

Focus on Commutative Rings Research

Ayman Badawi
Focus on Commutative Rings Research Book PDF

Author : Ayman Badawi
Publisher : Nova Publishers
Page : 220 pages
File Size : 46,6 Mb
Release : 2006
Category : Mathematics
ISBN : 1600210651

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Focus on Commutative Rings Research by Ayman Badawi Pdf

Focus on Commutative Rings Research

Multiplicative Ideal Theory and Factorization Theory

Scott Chapman,Marco Fontana,Alfred Geroldinger,Bruce Olberding
Multiplicative Ideal Theory and Factorization Theory Book PDF

Author : Scott Chapman,Marco Fontana,Alfred Geroldinger,Bruce Olberding
Publisher : Springer
Page : 407 pages
File Size : 54,6 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.

Rings, Polynomials, and Modules

Marco Fontana,Sophie Frisch,Sarah Glaz,Francesca Tartarone,Paolo Zanardo
Rings Polynomials and Modules Book PDF

Author : Marco Fontana,Sophie Frisch,Sarah Glaz,Francesca Tartarone,Paolo Zanardo
Publisher : Springer
Page : 375 pages
File Size : 46,7 Mb
Release : 2017-11-11
Category : Mathematics
ISBN : 9783319658742

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Rings, Polynomials, and Modules by Marco Fontana,Sophie Frisch,Sarah Glaz,Francesca Tartarone,Paolo Zanardo Pdf

This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non-Noetherian ring theory, module theory and integer-valued polynomials along with connections to algebraic number theory, algebraic geometry, topology and homological algebra. Most of the eighteen contributions are authored by attendees of the two conferences in commutative algebra that were held in the summer of 2016: “Recent Advances in Commutative Ring and Module Theory,” Bressanone, Italy; “Conference on Rings and Polynomials” Graz, Austria. There is also a small collection of invited articles authored by experts in the area who could not attend either of the conferences. Following the model of the talks given at these conferences, the volume contains a number of comprehensive survey papers along with related research articles featuring recent results that have not yet been published elsewhere.

Integers, Polynomials, and Rings

Ronald S. Irving
Integers Polynomials and Rings Book PDF

Author : Ronald S. Irving
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 40,8 Mb
Release : 2004-01-08
Category : Mathematics
ISBN : 9780387403977

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Integers, Polynomials, and Rings by Ronald S. Irving Pdf

This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an - dergraduatecourseinabstractalgebraoracoursedesignedasanintroduction to higher mathematics. This book di?ers from many undergraduate algebra texts in fundamental ways; the reasons lie in the book’s origin and the goals I set for the course. The course is a two-quarter sequence required of students intending to f- ?ll the requirements of the teacher preparation option for our B.A. degree in mathematics, or of the teacher preparation minor. It is required as well of those intending to matriculate in our university’s Master’s in Teaching p- gram for secondary mathematics teachers. This is the principal course they take involving abstraction and proof, and they come to it with perhaps as little background as a year of calculus and a quarter of linear algebra. The mathematical ability of the students varies widely, as does their level of ma- ematical interest.

Modern Analysis and Applications

Vadim Adamyan,Yu.M. Berezansky,Israel Gohberg,Myroslav L. Gorbachuk,Valentyna Gorbachuk,Anatoly N. Kochubei,Heinz Langer,Gennadi Popov
Modern Analysis and Applications Book PDF

Author : Vadim Adamyan,Yu.M. Berezansky,Israel Gohberg,Myroslav L. Gorbachuk,Valentyna Gorbachuk,Anatoly N. Kochubei,Heinz Langer,Gennadi Popov
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 52,5 Mb
Release : 2009-08-29
Category : Mathematics
ISBN : 9783764399214

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Modern Analysis and Applications by Vadim Adamyan,Yu.M. Berezansky,Israel Gohberg,Myroslav L. Gorbachuk,Valentyna Gorbachuk,Anatoly N. Kochubei,Heinz Langer,Gennadi Popov Pdf

This is the second of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.

Advances in Commutative Ring Theory

David Dobbs
Advances in Commutative Ring Theory Book PDF

Author : David Dobbs
Publisher : CRC Press
Page : 578 pages
File Size : 53,7 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."

A Guide to Groups, Rings, and Fields

Fernando Q. Gouvêa
A Guide to Groups Rings and Fields Book PDF

Author : Fernando Q. Gouvêa
Publisher : American Mathematical Soc.
Page : 309 pages
File Size : 44,5 Mb
Release : 2012-12-31
Category : Mathematics
ISBN : 9781614442110

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A Guide to Groups, Rings, and Fields by Fernando Q. Gouvêa Pdf

Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.

Groups, Rings, Modules

Maurice Auslander,David Buchsbaum
Groups Rings Modules Book PDF

Author : Maurice Auslander,David Buchsbaum
Publisher : Courier Corporation
Page : 484 pages
File Size : 40,9 Mb
Release : 2014-06-18
Category : Mathematics
ISBN : 9780486490823

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Groups, Rings, Modules by Maurice Auslander,David Buchsbaum Pdf

This classic monograph is geared toward advanced undergraduates and graduate students. The treatment presupposes some familiarity with sets, groups, rings, and vector spaces. The four-part approach begins with examinations of sets and maps, monoids and groups, categories, and rings. The second part explores unique factorization domains, general module theory, semisimple rings and modules, and Artinian rings. Part three's topics include localization and tensor products, principal ideal domains, and applications of fundamental theorem. The fourth and final part covers algebraic field extensions and Dedekind domains. Exercises are provided at the end of each chapter. Dover (2014) republication of the edition originally published by Harper & Row Publishers, New York, 1974. See every Dover book in print at www.doverpublications.com

Rings, Modules, Algebras, and Abelian Groups

Alberto Facchini,Evan Houston,Luigi Salce
Rings Modules Algebras and Abelian Groups Book PDF

Author : Alberto Facchini,Evan Houston,Luigi Salce
Publisher : CRC Press
Page : 530 pages
File Size : 54,6 Mb
Release : 2020-02-10
Category : Mathematics
ISBN : 0824750810

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Rings, Modules, Algebras, and Abelian Groups by Alberto Facchini,Evan Houston,Luigi Salce Pdf

Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological

Digital Signal Processing Algorithms

Hari Krishna
Digital Signal Processing Algorithms Book PDF

Author : Hari Krishna
Publisher : Routledge
Page : 664 pages
File Size : 40,6 Mb
Release : 2017-11-22
Category : Technology & Engineering
ISBN : 9781351454971

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Digital Signal Processing Algorithms by Hari Krishna Pdf

Digital Signal Processing Algorithms describes computational number theory and its applications to deriving fast algorithms for digital signal processing. It demonstrates the importance of computational number theory in the design of digital signal processing algorithms and clearly describes the nature and structure of the algorithms themselves. The book has two primary focuses: first, it establishes the properties of discrete-time sequence indices and their corresponding fast algorithms; and second, it investigates the properties of the discrete-time sequences and the corresponding fast algorithms for processing these sequences. Digital Signal Processing Algorithms examines three of the most common computational tasks that occur in digital signal processing; namely, cyclic convolution, acyclic convolution, and discrete Fourier transformation. The application of number theory to deriving fast and efficient algorithms for these three and related computationally intensive tasks is clearly discussed and illustrated with examples. Its comprehensive coverage of digital signal processing, computer arithmetic, and coding theory makes Digital Signal Processing Algorithms an excellent reference for practicing engineers. The authors' intent to demystify the abstract nature of number theory and the related algebra is evident throughout the text, providing clear and precise coverage of the quickly evolving field of digital signal processing.

An Introduction to Rings and Modules

A. J. Berrick,M. E. Keating
An Introduction to Rings and Modules Book PDF

Author : A. J. Berrick,M. E. Keating
Publisher : Cambridge University Press
Page : 286 pages
File Size : 48,6 Mb
Release : 2000-05
Category : Mathematics
ISBN : 0521632749

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An Introduction to Rings and Modules by A. J. Berrick,M. E. Keating Pdf

This is a concise 2000 introduction at graduate level to ring theory, module theory and number theory.

Selected Papers of S. A. Amitsur with Commentary

Shimshon A. Amitsur,Avinoam Mann
Selected Papers of S A Amitsur with Commentary Book PDF

Author : Shimshon A. Amitsur,Avinoam Mann
Publisher : American Mathematical Soc.
Page : 626 pages
File Size : 44,5 Mb
Release : 2001
Category : Mathematics
ISBN : 0821829246

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Selected Papers of S. A. Amitsur with Commentary by Shimshon A. Amitsur,Avinoam Mann Pdf

This handsomely-bound volume presents selected papers written by S.A. Amitsur on various topics in algebra. The approximately 50 papers in the first volume deal with general ring theory and rings satisfying a polynomial identity. A sampling of topics includes algebras over infinite fields, commutative linear differential operators, a generalization of Hilbert's Nullstellensatz, and central embeddings in semi-simple rings. Two essays on Amitsur's work and a biography also are included. The volume is not indexed. c. Book News Inc.

Rings, Monoids and Module Theory

Ayman Badawi,Jim Coykendall
Rings Monoids and Module Theory Book PDF

Author : Ayman Badawi,Jim Coykendall
Publisher : Springer Nature
Page : 317 pages
File Size : 50,8 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.