Del 0 - Graduate Studies in Mathematics

Graduate Algebra: Noncommutative View

Häftad, Engelska, 2008

1 399 kr

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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. The first half of the book can serve as a one-semester course on noncommutative algebra, whereas the remaining part of the book describes some of the major directions of research in the past 100 years. The main text is extended through several appendices, which permits the inclusion of more advanced material, and numerous exercises. The only prerequisite for using the book is an undergraduate course in algebra; whenever necessary, results are quoted from Graduate Algebra: Commutative View.

Produktinformation

Utgivningsdatum2008-10-31
FormatHäftad
SpråkEngelska
SerieGraduate Studies in Mathematics
Antal sidor648
FörlagAmerican Mathematical Society
ISBN9781470479039

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Algebra inom Naturvetenskap och teknik

Part IV. The structure of ringsIntroduction to the structure of ringsChapter 13. Fundamental concepts in ring theoryChapter 14. Semisimple modules and rings and the Wedderburn-Artin theoremChapter 15. The Jacobson program applied to left Artinian ringsChapter 16. Noetherian rings and the role of prime ringsChapter 17. Algebras in terms of generators and relationsChapter 18. Tensor productsExercises-Part IVPart V. Representations of groups and Lie algebrasIntroduction to representations of groups and Lie algebrasChapter 19. Group representations and group algebrasChapter 20. Characters of finite groupsChapter 21. Lie algebras and other nonassociative algebrasChapter 22. Dynkin diagrams (Coxeter-Dynkin graphs and Coxeter groups)Exercises-Part VPart VI. Representable algebrasIntroduction to representable algebrasChapter 23. Polynomial identities and representable algebrasChapter 24. Central simple algebras and the Brauer groupChapter 25. Homological algebra and categories of modulesChapter 26. Hopf algebrasExercises-Part VI

Each part ends with more than 30 pages of exercises, from the basic to the challenging, carefully arranged and labeled according to the chapter (or appendix) to which they related ... a striking and very enjoyable feature of the book is the huge number of digressions: there are frequent pauses to point out noteworthy aspects of the terrain which lies ahead, beyond what can be covered in detail in a book of this sort. The style, layout and precision of the book make it a pleasure to read... -- Mathematical Reviews The book is largely self-contained. ...a valuable textbook and a reliable reference for graduate students. -- MAA Reviews