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Benson Farb, R. Keith Dennis, "Noncommutative Algebra"

This book is an introduction to the theory of noncommutative algebra. The core of the book is suitable for a one-semester course for graduate students. The approach, which is more homological than ring-theoretic, clarifies the subject and its relation to other important areas of mathematics, including K-theory, homological algebra, and representation theory. The main part of the book begins with a brief review of background material; the first chapter covers the basics of semisimple modules and rings, including the Wedderburn structure theorem; chapter two discusses the Jacobson radical, giving several different views; chapter three develops the theory of central simple algebras, including proofs of the Skolem-Noether and Double Centralizer theorems, with two famous theorems of Wedderburn and Frobenius given as applications; and chapter four is an introduction to the Brauer group and its relation to cohomology. The remaining chapters introduce several special topics: the notion of primitive ring is developed along lines parallel to that of simple rings; the representation theory of finite groups is combined with the Wedderburn Structure Theorem to prove Burnside's Theorem; the global dimension of a ring is studied using Kaplansky's elementary point of view; and the Brauer group of a commutative ring is introduced. Problems throughout the book provide concrete examples, applications and amplifications of the text; a set of supplementary problems explores further topics and can serve as starting points for student projects.

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	Science/Engineering A First Course in Noncommutative Rings A First Course in Noncommutative RingsSpringer 2 edition \| 2001 \| 408 pages \| ISBN-10: 0387953256 \| DJVU \| 5.19 MBThis book, an outgrowth of the author?s lectures at the University of California at Berkeley, is intended as a textbook for a ...
	Science/Engineering Geometric Models for Noncommutative Algebra Geometric Models for Noncommutative AlgebraAmerican Mathematical Society \| June 1999 \| ISBN-10: 0821809520 \| 184 pages \| PDF \| 4.3 mbThe volume is based on a course, "Geometric Models for Noncommutative Algebras" taught by Professor Weinste ...
	Science/Engineering Noncommutative Spacetimes: Symmetries in Noncommutative Geometry and Field Theory P. Aschieri, M. Dimitrijevic, P. Kulish, F. Lizzi, J. Wess, "Noncommutative Spacetimes: Symmetries in Noncommutative Geometry and Field Theory"Springer \| 2009-08-01 \| ISBN: 3540897925 \| 199 pages \| PDF \| 1,2 MBThere are many approaches ...
	Algebra Through Practice: Volume 4, Linear Algebra: A Collection of Problems in Algebra with Solutions T. S. Blyth, E. F. Robertson, "Algebra Through Practice: Volume 4, Linear Algebra: A Collection of Problems in Algebra with Solutions" Cambridge University Press \| 1985 \| ISBN: 0521272890 \| 116 pages \| PDF \| 1,2 MB Problem-solving is an ...
	Computational Noncommutative Algebra and Applications: Proceedings of the NATO Advanced Study Institute, on Computatoinal Noncommutative Algebra and Applications, ... II: Mathematics, Physics and Chemistry) Author: Publisher: Springer (2004)Binding: Hardcover, 427 pagespricer: $229.00ISBN-10: 1402019823editorialreviewsThe fusion of algebra, analysis and geometry, and their application to real world problems, have been dominant themes underlyin ...
	Technical Noncommutative Algebra and Geometry Corrado De Concini, Freddy Van Oystaeyen, Nikolai Vavilov, Anatoly Yakovlev, "Noncommutative Algebra and Geometry" Chapman & Hall/CRC \| 2005 \| ISBN: 082472349X \| 272 pages \| PDF \| 2,6 MB A valuable addition to the Lecture Notes in P ...

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