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An Introduction To Noncommutative Noetherian Rings

Author: K. R. Goodearl
Publisher: Cambridge University Press
ISBN: 9780521545372
Size: 57.91 MB
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This introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.

New Trends In Noncommutative Algebra

Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 0821852973
Size: 19.33 MB
Format: PDF, ePub
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This volume contains the proceedings of the conference ``New Trends in Noncommutative Algebra'', held at the University of Washington, Seattle, in August 2010, in honor of Ken Goodearl's 65th birthday. The articles reflect the wide interests of Goodearl and will provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Calabi-Yau algebras, quantum algebras and deformation quantization, Poisson algebras, growth of algebras, group algebras, and noncommutative Iwasawa algebras.

Non Commutative Ring Theory

Author: Surender K. Jain
Publisher: Springer
ISBN: 3540467459
Size: 43.53 MB
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The papers of this volume share as a common goal the structure and classi- fication of noncommutative rings and their modules, and deal with topics of current research including: localization, serial rings, perfect endomorphism rings, quantum groups, Morita contexts, generalizations of injectivitiy, and Cartan matrices.

Advances In Rings And Modules

Author: Sergio R. López-Permouth
Publisher: American Mathematical Soc.
ISBN: 1470435551
Size: 35.62 MB
Format: PDF
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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.

Lmsst 24 Lectures On Elliptic Curves

Author: John William Scott Cassels
Publisher: Cambridge University Press
ISBN: 9780521425308
Size: 66.67 MB
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The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Wei finite basis theorem, points of finite order (Nagell-Lutz), etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction.

A Primer Of Algebraic D Modules

Author: S. C. Coutinho
Publisher: Cambridge University Press
ISBN: 9780521559089
Size: 63.95 MB
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The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications, avoiding all unnecessary technicalities. The author takes an algebraic approach, concentrating on the role of the Weyl algebra. The author assumes very few prerequisites, and the book is virtually self-contained. The author includes exercises at the end of each chapter and gives the reader ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.

Hyperbolic Geometry

Author: Birger Iversen
Publisher: Cambridge University Press
ISBN: 0521435080
Size: 13.65 MB
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Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon theorem and the relationship between hyperbolic geometries and discrete groups of isometries. Hyperbolic 3-space is also discussed, and the directions that current research in this field is taking are sketched. This will be an excellent introduction to hyperbolic geometry for students new to the subject, and for experts in other fields.