This book is a companion volume to Graduate Algebra: Commutative View (published as volume 73 in this series). The main and most important feature of the book is that it presents a unified approach to many important topics, such as group theory, ring theory, Lie algebras, and gives conceptual proofs of many basic results of noncommutative algebra. There are also a number of major results in noncommutative algebra that are usually found only in technical works, such as Zelmanov's proof of the restricted Burnside problem in group theory, word problems in groups, Tits's alternative in algebraic groups, PI algebras, and many of the roles that Coxeter diagrams play in algebra.
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978-0-8218-4153-2 (9780821841532)
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Schweitzer Klassifikation
The structure of rings: Fundamental concepts in ring theory Semisimple modules and rings and the Wedderburn-Artin theorem The Jacobson program applied to left Artinian rings Noetherian rings and the role of prime rings Algebras in terms of generators and relations Tensor products Exercises-Part IV Representations of groups and Lie algebras: Group representations and group algebras Characters of finite groups Lie algebras and other nonassociative algebras Dynkin diagrams (Coxeter-Dynkin graphs and Coxeter groups) Exercises-Part V Representable algebras: Polynomial identities and representable algebras Central simple algebras and the Brauer group Homological algebra and categories of modules Hopf algebras Exercises-Part VI Bibliography Index.
