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Free Ideal Rings And Localization In General Rings
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Book Synopsis Free Ideal Rings and Localization in General Rings by : P. M. Cohn
Download or read book Free Ideal Rings and Localization in General Rings written by P. M. Cohn and published by Cambridge University Press. This book was released on 2006-06-08 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.
Book Synopsis Free Ideal Rings and Localization in General Rings by : P. M. Cohn
Download or read book Free Ideal Rings and Localization in General Rings written by P. M. Cohn and published by Cambridge University Press. This book was released on 2006-06-08 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention.
Book Synopsis Noncommutative Localization in Algebra and Topology by : Andrew Ranicki
Download or read book Noncommutative Localization in Algebra and Topology written by Andrew Ranicki and published by Cambridge University Press. This book was released on 2006-02-09 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.
Book Synopsis Advances in Rings and Modules by : Sergio R. López-Permouth
Download or read book Advances in Rings and Modules written by Sergio R. López-Permouth and published by American Mathematical Soc.. This book was released on 2018-09-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.
Book Synopsis Purity, Spectra and Localisation by : Mike Prest
Download or read book Purity, Spectra and Localisation written by Mike Prest and published by Cambridge University Press. This book was released on 2009-06-04 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches.
Book Synopsis Integral Closure of Ideals, Rings, and Modules by : Craig Huneke
Download or read book Integral Closure of Ideals, Rings, and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Book Synopsis An Invitation to General Algebra and Universal Constructions by : George M. Bergman
Download or read book An Invitation to General Algebra and Universal Constructions written by George M. Bergman and published by Springer. This book was released on 2015-02-05 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
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 414 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 with Polynomial Identities and Finite Dimensional Representations of Algebras by : Eli Aljadeff
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 :Dmitry S. Kaliuzhnyi-Verbovetskyi Publisher :American Mathematical Soc. ISBN 13 :1470416972 Total Pages :194 pages Book Rating :4.4/5 (74 download)
Book Synopsis Foundations of Free Noncommutative Function Theory by : Dmitry S. Kaliuzhnyi-Verbovetskyi
Download or read book Foundations of Free Noncommutative Function Theory written by Dmitry S. Kaliuzhnyi-Verbovetskyi and published by American Mathematical Soc.. This book was released on 2014-11-19 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.
Book Synopsis Computation and Combinatorics in Dynamics, Stochastics and Control by : Elena Celledoni
Download or read book Computation and Combinatorics in Dynamics, Stochastics and Control written by Elena Celledoni and published by Springer. This book was released on 2019-01-13 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.
Book Synopsis Semidefinite Optimization and Convex Algebraic Geometry by : Grigoriy Blekherman
Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2012-01-01 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained, accessible introduction to the mathematical advances and challenges resulting from the use of semidefinite programming in polynomial optimization. This quickly evolving research area with contributions from the diverse fields of convex geometry, algebraic geometry, and optimization is known as convex algebraic geometry. Each chapter addresses a fundamental aspect of convex algebraic geometry. The book begins with an introduction to nonnegative polynomials and sums of squares and their connections to semidefinite programming and quickly advances to several areas at the forefront of current research. These include (1) semidefinite representability of convex sets, (2) duality theory from the point of view of algebraic geometry, and (3) nontraditional topics such as sums of squares of complex forms and noncommutative sums of squares polynomials. Suitable for a class or seminar, with exercises aimed at teaching the topics to beginners, Semidefinite Optimization and Convex Algebraic Geometry serves as a point of entry into the subject for readers from multiple communities such as engineering, mathematics, and computer science. A guide to the necessary background material is available in the appendix.
Book Synopsis Free Rings and Their Relations by : Paul Moritz Cohn
Download or read book Free Rings and Their Relations written by Paul Moritz Cohn and published by . This book was released on 1985 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry, Topology, and Dynamics in Negative Curvature by : C. S. Aravinda
Download or read book Geometry, Topology, and Dynamics in Negative Curvature written by C. S. Aravinda and published by Cambridge University Press. This book was released on 2016-01-21 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ICM 2010 satellite conference 'Geometry, Topology and Dynamics in Negative Curvature' afforded an excellent opportunity to discuss various aspects of this fascinating interdisciplinary subject in which methods and techniques from geometry, topology, and dynamics often interact in novel and interesting ways. Containing ten survey articles written by some of the leading experts in the field, this proceedings volume provides an overview of important recent developments relating to negative curvature. Topics covered include homogeneous dynamics, harmonic manifolds, the Atiyah Conjecture, counting circles and arcs, and hyperbolic buildings. Each author pays particular attention to the expository aspects, making the book particularly useful for graduate students and mathematicians interested in transitioning from other areas via the common theme of negative curvature.
Book Synopsis Groups St Andrews 2017 in Birmingham by : C. M. Campbell
Download or read book Groups St Andrews 2017 in Birmingham written by C. M. Campbell and published by Cambridge University Press. This book was released on 2019-04-11 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.
Book Synopsis Noncommutative Rational Series with Applications by : Jean Berstel
Download or read book Noncommutative Rational Series with Applications written by Jean Berstel and published by Cambridge University Press. This book was released on 2011 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern account of the subject and its applications. Excellent resource for those working in algebra and theoretical computer science.
Book Synopsis Lattice Theory: Foundation by : George Grätzer
Download or read book Lattice Theory: Foundation written by George Grätzer and published by Springer Science & Business Media. This book was released on 2011-02-14 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Almost 40 “diamond sections’’, many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics. “Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication.” Bulletin of the American Mathematical Society “Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” Mathematical Reviews
