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Algebraic Number Theoretic And Topological Aspects Of Ring Theory
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Book Synopsis Algebraic, Number Theoretic, and Topological Aspects of Ring Theory by : Jean-Luc Chabert
Download or read book Algebraic, Number Theoretic, and Topological Aspects of Ring Theory written by Jean-Luc Chabert and published by Springer Nature. This book was released on 2023-07-07 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Certain Number-Theoretic Episodes in Algebra by : R Sivaramakrishnan
Download or read book Certain Number-Theoretic Episodes in Algebra written by R Sivaramakrishnan and published by CRC Press. This book was released on 2019-08-30 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Twelve Papers on Topology, Algebra and Number Theory by :
Download or read book Twelve Papers on Topology, Algebra and Number Theory written by and published by American Mathematical Soc.. This book was released on 1966-12-31 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis American Mathematical Society Translations by : S. P. Demuškin
Download or read book American Mathematical Society Translations written by S. P. Demuškin and published by American Mathematical Soc.. This book was released on 1966 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Commutative Algebra and Number Theory by : Sukumar Das Adhikari
Download or read book An Introduction to Commutative Algebra and Number Theory written by Sukumar Das Adhikari and published by CRC Press. This book was released on 2001-11 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Brief Guide to Algebraic Number Theory by : H. P. F. Swinnerton-Dyer
Download or read book A Brief Guide to Algebraic Number Theory written by H. P. F. Swinnerton-Dyer and published by Cambridge University Press. This book was released on 2001-02-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author :Gary F. Birkenmeier Publisher :Springer Science & Business Media ISBN 13 :9780817641580 Total Pages :468 pages Book Rating :4.6/5 (415 download)
Book Synopsis International Symposium on Ring Theory by : Gary F. Birkenmeier
Download or read book International Symposium on Ring Theory written by Gary F. Birkenmeier and published by Springer Science & Business Media. This book was released on 2001 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Exercises in Cellular Automata and Groups by : Tullio Ceccherini-Silberstein
Download or read book Exercises in Cellular Automata and Groups written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2023-11-01 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Ring Theory written by and published by Academic Press. This book was released on 1972-04-18 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ring Theory
Book Synopsis Multiplicative Ideal Theory and Factorization Theory by : Scott Chapman
Download or read book Multiplicative Ideal Theory and Factorization Theory written by Scott Chapman and published by Springer. This book was released on 2016-07-29 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Rings, Polynomials, and Modules by : Marco Fontana
Download or read book Rings, Polynomials, and Modules written by Marco Fontana and published by Springer. This book was released on 2017-11-11 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Number Theory by : Richard A. Mollin
Download or read book Algebraic Number Theory written by Richard A. Mollin and published by CRC Press. This book was released on 1999-03-16 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its history as an elegant but abstract area of mathematics, algebraic number theory now takes its place as a useful and accessible study with important real-world practicality. Unique among algebraic number theory texts, this important work offers a wealth of applications to cryptography, including factoring, primality-testing, and public-key cryptosystems. A follow-up to Dr. Mollin's popular Fundamental Number Theory with Applications, Algebraic Number Theory provides a global approach to the subject that selectively avoids local theory. Instead, it carefully leads the student through each topic from the level of the algebraic integer, to the arithmetic of number fields, to ideal theory, and closes with reciprocity laws. In each chapter the author includes a section on a cryptographic application of the ideas presented, effectively demonstrating the pragmatic side of theory. In this way Algebraic Number Theory provides a comprehensible yet thorough treatment of the material. Written for upper-level undergraduate and graduate courses in algebraic number theory, this one-of-a-kind text brings the subject matter to life with historical background and real-world practicality. It easily serves as the basis for a range of courses, from bare-bones algebraic number theory, to a course rich with cryptography applications, to a course using the basic theory to prove Fermat's Last Theorem for regular primes. Its offering of over 430 exercises with odd-numbered solutions provided in the back of the book and, even-numbered solutions available a separate manual makes this the ideal text for both students and instructors.
Book Synopsis Algebraic Number Theory by : Jürgen Neukirch
Download or read book Algebraic Number Theory written by Jürgen Neukirch and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.
Book Synopsis Algebras, Rings and Modules by : Michiel Hazewinkel
Download or read book Algebras, Rings and Modules written by Michiel Hazewinkel and published by CRC Press. This book was released on 2016-04-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.
Book Synopsis Topological Fields and Near Valuations by : Niel Shell
Download or read book Topological Fields and Near Valuations written by Niel Shell and published by CRC Press. This book was released on 2021-06-23 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part I (eleven chapters) of this text for graduate students provides a Survey of topological fields, while Part II (five chapters) provides a relatively more idiosyncratic account of valuation theory.
Download or read book Handbook of Algebra written by and published by Elsevier. This book was released on 2003-10-15 with total page 1184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Algebra
Book Synopsis Algebraic Number Theory and Algebraic Geometry by : S. V. Vostokov
Download or read book Algebraic Number Theory and Algebraic Geometry written by S. V. Vostokov and published by American Mathematical Soc.. This book was released on 2002-09-19 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A. N. Parshin is a world-renowned mathematician who has made significant contributions to number theory through the use of algebraic geometry. Articles in this volume present new research and the latest developments in algebraic number theory and algebraic geometry and are dedicated to Parshin's sixtieth birthday. Well-known mathematicians contributed to this volume, including, among others, F. Bogomolov, C. Deninger, and G. Faltings. The book is intended for graduate students and research mathematicians interested in number theory, algebra, and algebraic geometry.
