Noncommutative Algebra

Benson Farb, R. Keith Dennis (Autoren)

Buch | Softcover

226 Seiten

2012 | Softcover reprint of the original 1st ed. 1993
Springer-Verlag New York Inc.
978-1-4612-6936-6 (ISBN)

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About This Book This book is meant to be used by beginning graduate students. It covers basic material needed by any student of algebra, and is essential to those specializing in ring theory, homological algebra, representation theory and K-theory, among others. It will also be of interest to students of algebraic topology, functional analysis, differential geometry and number theory. Our approach is more homological than ring-theoretic, as this leads the to many important areas of mathematics. This ap student more quickly proach is also, we believe, cleaner and easier to understand. However, the more classical, ring-theoretic approach, as well as modern extensions, are also presented via several exercises and sections in Chapter Five. We have tried not to leave any gaps on the paths to proving the main theorem- at most we ask the reader to fill in details for some of the sideline results; indeed this can be a fruitful way of solidifying one's understanding.

I The Core Course.- 0 Background Material.- 1 Semisimple Modules & Rings and the Wedderburn Structure Theorem.- 2 The Jacobson Radical.- 3 Central Simple Algebras.- 4 The Brauer Group.- II Selected Topics.- 5 Primitive Rings and the Density Theorem.- 6 Burnside’s Theorem and Representations of Finite Groups.- 7 The Global Dimension of a Ring.- 8 The Brauer Group of a Commutative Ring.- III Supplementary Exercises.- References.

Reihe/Serie	Graduate Texts in Mathematics ; 144
Zusatzinfo	XIV, 226 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-10	1-4612-6936-9 / 1461269369
ISBN-13	978-1-4612-6936-6 / 9781461269366
Zustand	Neuware