Noncommutative Algebra (Graduate Texts in Mathematics) - Softcover

Farb, Benson; Dennis, R. Keith

Softcover

ISBN 10: 354094057X ISBN 13: 9783540940579

Verlag: Springer Berlin, 1993

Inhaltsangabe

This book is an introduction to the theory of non-commutative 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 semi-simple modules and rings, including the Wedderbum 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 fugte 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.

Details zur Ausgabe

• Verlag: Springer Berlin
• Erscheinungsdatum: 1993
• Sprache: Englisch
• ISBN 10: 354094057X
• ISBN 13: 9783540940579
• Einband: Taschenbuch
• Anzahl der Seiten: 237
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland