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Author : Taylor & Francis Group
Publisher :
ISBN 13 : 9781138098510
Total Pages : pages
Book Rating : 4.0/5 (985 download)
Download or read book Finite Commutative Rings and Their Polynomial Rings written by Taylor & Francis Group and published by . This book was released on 2018-10-06 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gilberto Bini
Publisher : Springer Science & Business Media
ISBN 13 : 1461509572
Total Pages : 181 pages
Book Rating : 4.4/5 (615 download)
Download or read book Finite Commutative Rings and Their Applications written by Gilberto Bini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.
Author : Eli Aljadeff
Publisher : American Mathematical Soc.
ISBN 13 : 1470451743
Total Pages : 630 pages
Book Rating : 4.4/5 (74 download)
Download or read book Rings with Polynomial Identities and Finite Dimensional Representations of Algebras written by Eli Aljadeff and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: A polynomial identity for an algebra (or a ring) A A is a polynomial in noncommutative variables that vanishes under any evaluation in A A. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley–Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
Author : Marco Fontana
Publisher : Springer
ISBN 13 : 1493909258
Total Pages : 372 pages
Book Rating : 4.4/5 (939 download)
Download or read book Commutative Algebra written by Marco Fontana and published by Springer. This book was released on 2014-07-15 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. 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 as well as integer-valued polynomials and functions. Specific topics include: · Homological dimensions of Prüfer-like rings · Quasi complete rings · Total graphs of rings · Properties of prime ideals over various rings · Bases for integer-valued polynomials · Boolean subrings · The portable property of domains · Probabilistic topics in Intn(D) · Closure operations in Zariski-Riemann spaces of valuation domains · Stability of domains · Non-Noetherian grade · Homotopy in integer-valued polynomials · Localizations of global properties of rings · Topics in integral closure · Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.
Author : Vesselin Drensky
Publisher : Birkhäuser
ISBN 13 : 3034879342
Total Pages : 197 pages
Book Rating : 4.0/5 (348 download)
Download or read book Polynomial Identity Rings written by Vesselin Drensky and published by Birkhäuser. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject.
Author : Marco Fontana
Publisher : Springer
ISBN 13 : 3319658743
Total Pages : 374 pages
Book Rating : 4.3/5 (196 download)
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 374 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.
Author : Melvin Hochster
Publisher : American Mathematical Soc.
ISBN 13 : 9780821888711
Total Pages : 88 pages
Book Rating : 4.8/5 (887 download)
Download or read book Topics in the Homological Theory of Modules Over Commutative Rings written by Melvin Hochster and published by American Mathematical Soc.. This book was released on 1975-12-31 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains expository lectures by Melvin Hochster from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. The lectures deal mainly with recent developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings. A good deal of attention is given to the role ``big'' Cohen-Macaulay modules play in clearing up some of the open questions. A modest knowledge of commutative rings and familarity with (the long exact sequences for) Tor and Ext should suffice as a background for the reader.
Author : Bernard R. McDonald
Publisher :
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.:/5 (44 download)
Download or read book Finite Rings with Identity written by Bernard R. McDonald and published by . This book was released on 1974 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I. N. Herstein
Publisher : American Mathematical Soc.
ISBN 13 : 088385015X
Total Pages : 202 pages
Book Rating : 4.8/5 (838 download)
Download or read book Noncommutative Rings written by I. N. Herstein and published by American Mathematical Soc.. This book was released on 1994-12-31 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Rings provides a cross-section of ideas, techniques, and results that give the reader an idea of that part of algebra which concerns itself with noncommutative rings. In the space of 200 pages, Herstein covers the Jacobson radical, semisimple rings, commutativity theorems, simple algebras, representations of finite groups, polynomial identities, Goldie's theorem, and the Golod–Shafarevitch theorem. Almost every practicing ring theorist has studied portions of this classic monograph.
Author : Masayoshi Nagata
Publisher : American Mathematical Soc.
ISBN 13 : 9780821816875
Total Pages : 44 pages
Book Rating : 4.8/5 (168 download)
Download or read book Polynomial Rings and Affine Spaces written by Masayoshi Nagata and published by American Mathematical Soc.. This book was released on 1978 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains expository lectures from the Conference Board of the Mathematical Sciences Regional Conference held at Northern Illinois University on July 25-29, 1977.
Author : Andy R. Magid
Publisher : CRC Press
ISBN 13 : 1482208067
Total Pages : 184 pages
Book Rating : 4.4/5 (822 download)
Download or read book The Separable Galois Theory of Commutative Rings written by Andy R. Magid and published by CRC Press. This book was released on 2014-07-14 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Separable Galois Theory of Commutative Rings, Second Edition provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a n
Author : John J. Watkins
Publisher : Princeton University Press
ISBN 13 : 1400828171
Total Pages : 228 pages
Book Rating : 4.4/5 (8 download)
Download or read book Topics in Commutative Ring Theory written by John J. Watkins and published by Princeton University Press. This book was released on 2009-02-09 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra. Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian rings-one of the most important classes of commutative rings--and beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active reading--routine exercises as well as problems that build technical skills and reinforce new concepts. The final chapter is devoted to new computational techniques now available through computers. Careful to avoid intimidating theorems and proofs whenever possible, Watkins emphasizes the historical roots of the subject, like the role of commutative rings in Fermat's last theorem. He leads readers into unexpected territory with discussions on rings of continuous functions and the set-theoretic foundations of mathematics. Written by an award-winning teacher, this is the first introductory textbook to require no prior knowledge of ring theory to get started. Refreshingly informal without ever sacrificing mathematical rigor, Topics in Commutative Ring Theory is an ideal resource for anyone seeking entry into this stimulating field of study.
Author :
Publisher : Academic Press
ISBN 13 : 0080874002
Total Pages : 387 pages
Book Rating : 4.0/5 (88 download)
Download or read book Polynomial Identities in Ring Theory written by and published by Academic Press. This book was released on 1980-07-24 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial Identities in Ring Theory
Author : Irving Kaplansky
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.4/5 (91 download)
Download or read book Commutative Rings written by Irving Kaplansky and published by . This book was released on 1970 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Marco Fontana
Publisher : CRC Press
ISBN 13 : 9780203910627
Total Pages : 524 pages
Book Rating : 4.9/5 (16 download)
Download or read book Commutative Ring Theory and Applications written by Marco Fontana and published by CRC Press. This book was released on 2017-07-27 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra. With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory, geome
Author : Ali Benhissi
Publisher : Springer Nature
ISBN 13 : 3031098986
Total Pages : 529 pages
Book Rating : 4.0/5 (31 download)
Download or read book Chain Conditions in Commutative Rings written by Ali Benhissi and published by Springer Nature. This book was released on 2022-10-07 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers, in a beautifully structured way, recent findings on chain conditions in commutative algebra that were previously only available in papers. The majority of chapters are self-contained, and all include detailed proofs, a wealth of examples and solved exercises, and a complete reference list. The topics covered include S-Noetherian, S-Artinian, Nonnil-Noetherian, and Strongly Hopfian properties on commutative rings and their transfer to extensions such as polynomial and power series rings, and more. Though primarily intended for readers with a background in commutative rings, modules, polynomials and power series extension rings, the book can also be used as a reference guide to support graduate-level algebra courses, or as a starting point for further research.
Author : Grigore Calugareanu
Publisher : Springer Science & Business Media
ISBN 13 : 9401590044
Total Pages : 193 pages
Book Rating : 4.4/5 (15 download)
Download or read book Exercises in Basic Ring Theory written by Grigore Calugareanu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each undergraduate course of algebra begins with basic notions and results concerning groups, rings, modules and linear algebra. That is, it begins with simple notions and simple results. Our intention was to provide a collection of exercises which cover only the easy part of ring theory, what we have named the "Basics of Ring Theory". This seems to be the part each student or beginner in ring theory (or even algebra) should know - but surely trying to solve as many of these exercises as possible independently. As difficult (or impossible) as this may seem, we have made every effort to avoid modules, lattices and field extensions in this collection and to remain in the ring area as much as possible. A brief look at the bibliography obviously shows that we don't claim much originality (one could name this the folklore of ring theory) for the statements of the exercises we have chosen (but this was a difficult task: indeed, the 28 titles contain approximatively 15.000 problems and our collection contains only 346). The real value of our book is the part which contains all the solutions of these exercises. We have tried to draw up these solutions as detailed as possible, so that each beginner can progress without skilled help. The book is divided in two parts each consisting of seventeen chapters, the first part containing the exercises and the second part the solutions.
