Algebraic, Number Theoretic, and Topological Aspects of Ring Theory

Algebraic, Number Theoretic, and Topological Aspects of Ring Theory PDF

Author: Jean-Luc Chabert

Publisher: Springer Nature

Published: 2023-07-07

Total Pages: 473

ISBN-13: 3031288475

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This volume has been curated from two sources: presentations from the Conference on Rings and Polynomials, Technische Universität Graz, Graz, Austria, July 19 –24, 2021, and papers intended for presentation at the Fourth International Meeting on Integer-valued Polynomials and Related Topics, CIRM, Luminy, France, which was cancelled due to the pandemic. The collection ranges widely over the algebraic, number theoretic and topological aspects of rings, algebras and polynomials. Two areas of particular note are topological methods in ring theory, and integer valued polynomials. The book is dedicated to the memory of Paul-Jean Cahen, a coauthor or research collaborator with some of the conference participants and a friend to many of the others. This collection contains a memorial article about Paul-Jean Cahen, written by his longtime research collaborator and coauthor Jean-Luc Chabert.

Certain Number-Theoretic Episodes in Algebra

Certain Number-Theoretic Episodes in Algebra PDF

Author: R Sivaramakrishnan

Publisher: CRC Press

Published: 2019-08-30

Total Pages: 632

ISBN-13: 9780367390327

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Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available. Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.

An Introduction to Commutative Algebra and Number Theory

An Introduction to Commutative Algebra and Number Theory PDF

Author: Sukumar Das Adhikari

Publisher: CRC Press

Published: 2001-11

Total Pages: 176

ISBN-13: 9780849309908

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This is an elementary introduction to algebra and number theory. The text begins by a review of groups, rings, and fields. The algebra portion addresses polynomial rings, UFD, PID, and Euclidean domains, field extensions, modules, and Dedckind domains. The number theory portion reviews elementary congruence, quadratic reciprocity, algebraic number fields, and a glimpse into the various aspects of that subject. This book could be used as a one semester course in graduate mathematics.

A Brief Guide to Algebraic Number Theory

A Brief Guide to Algebraic Number Theory PDF

Author: H. P. F. Swinnerton-Dyer

Publisher: Cambridge University Press

Published: 2001-02-22

Total Pages: 164

ISBN-13: 9780521004237

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Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

International Symposium on Ring Theory

International Symposium on Ring Theory PDF

Author: Gary F. Birkenmeier

Publisher: Springer Science & Business Media

Published: 2001

Total Pages: 468

ISBN-13: 9780817641580

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Ring theory provides the algebraic underpinnings for many areas of mathematics, computer science, and physics. For example, ring theory appears in: functional analysis; algebraic topology; algebraic number theory; coding theory; and in the study of quantum theory. This volume is a collection of research papers, many presented at the 3rd Korea-China-Japan International Symposium on Ring Theory held jointly with the 2nd Korea-Japan Ring Theory Seminar, in Korea, The articles examine wide-ranging developments and methodologies in various areas, including classical Hopf algebras and quantum groups.

Multiplicative Ideal Theory and Factorization Theory

Multiplicative Ideal Theory and Factorization Theory PDF

Author: Scott Chapman

Publisher: Springer

Published: 2016-07-29

Total Pages: 407

ISBN-13: 331938855X

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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.

Exercises in Cellular Automata and Groups

Exercises in Cellular Automata and Groups PDF

Author: Tullio Ceccherini-Silberstein

Publisher: Springer Nature

Published: 2023-11-01

Total Pages: 638

ISBN-13: 3031103912

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This book complements the authors’ monograph Cellular Automata and Groups [CAG] (Springer Monographs in Mathematics). It consists of more than 600 fully solved exercises in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of gradually worked out examples and counterexamples presented here for the first time in textbook form. Additional comments provide some historical and bibliographical information, including an account of related recent developments and suggestions for further reading. The eight-chapter division from [CAG] is maintained. Each chapter begins with a summary of the main definitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use. Foreword by Rostislav I. Grigorchuk

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