free ideal rings and localization in general rings new mathematical monographs

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Free Ideal Rings And Localization In General Rings

Author : P. M. Cohn
ISBN : 9781139454995
Genre : Mathematics
File Size : 71. 78 MB
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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.

Advances In Rings And Modules

Author : Sergio R. López-Permouth
ISBN : 9781470435554
Genre : Modules (Algebra)
File Size : 64. 3 MB
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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.

Purity Spectra And Localisation

Author : Mike Prest
ISBN : 9781139643894
Genre : Mathematics
File Size : 84. 38 MB
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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.

Multiplicative Ideal Theory And Factorization Theory

Author : Scott Chapman
ISBN : 9783319388557
Genre : Mathematics
File Size : 31. 39 MB
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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.

An Invitation To General Algebra And Universal Constructions

Author : George M. Bergman
ISBN : 9783319114781
Genre : Mathematics
File Size : 81. 61 MB
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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.

Mathematical Reviews

Author :
ISBN : UOM:39015078588608
Genre : Mathematics
File Size : 31. 99 MB
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Groups Rings Modules

Author : Maurice Auslander
ISBN : 9780486795423
Genre : Mathematics
File Size : 76. 52 MB
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Classic monograph covers sets and maps, monoids and groups, unique factorization domains, localization and tensor products, applications of fundamental theorem, algebraic field extension, Dedekind domains, and much more. 1974 edition.

Rings And Factorization

Author : David Sharpe
ISBN : 0521337186
Genre : Mathematics
File Size : 40. 94 MB
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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.

Skew Fields

Author : Paul Moritz Cohn
ISBN : 0521432170
Genre : Mathematics
File Size : 37. 88 MB
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This work offers a comprehensive account of skew fields and related mathematics.

Noetherian Rings And Their Applications

Author : Lance W. Small
ISBN : 9780821815250
Genre : Mathematics
File Size : 88. 92 MB
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Researchers in ring theory or allied topics, such as the representation theory of finite dimensional Lie algebras, will appreciate this collection of expository lectures on advances in ring theory and their applications to other areas. Five of the lectures were delivered at a conference on Noetherian rings at the Mathematisches Forschungsinstitut, Oberwolfach, in January 1983, and the sixth was delivered at a London Mathematical Society Durham conference in July 1983. The study of the prime and primitive ideal spectra of various classes of rings forms a common theme in the lectures, and they touch on such topics as the structure of group rings of polycyclic-by-finite groups, localization in non commutative rings, and rings of differential operators. The lectures require the background of an advanced graduate student in ring theory and may be used in seminars in ring theory at this level.

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