Noncommutative algebra. Graduate Texts in Mathematics; 144.

Farb, Benson:

ISBN 10: 354094057X / ISBN 13: 9783540940579

Published by New York, Springer-Verlag, 1993

About this Item

xiv, 223 p. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-04627 354094057X Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2490865

Bibliographic Details

• Title: Noncommutative algebra. Graduate Texts in Mathematics; 144.
• Publisher: New York, Springer-Verlag
• Publication Date: 1993
• Language: English
• ISBN 10: 354094057X
• ISBN 13: 9783540940579
• Binding: Hardcover
• Weight: 550 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

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 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.