Algebra: An Approach Via Module Theory - Couverture rigide

Adkins, W.A.; Weintraub, Steven H.

Couverture rigide

ISBN 10 : 3540978399 ISBN 13 : 9783540978398

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1999

Synopsis

This book is designed as a text for a first-year undergraduate-level course in algebra. Instead of an encyclopaedic approach, the authors use a thematic, consistent point of view. The unifying theme is the concept of a module. To promote understanding, the book provides proofs with a maximum of insight and a minimum of computation, as well as chapters stressing computational techniques. Beginning with an introduction to group theory and ring theory, the book then develops the basics of module theory. A review of the basics of linear algebra demonstrates the power of module theory in the derivation of canonical forms and the spectral theorem. The book then uses module theory to investigate bilinear, sesquilinear and quadratic forms. Finally, a discussion of ring theory and multilinear forms leads to a chapter on group representations, which again uses module theory to powerful effect.

A propos du livre

Présentation de l'éditeur

This book is designed as a text for a first-year graduate algebra course. The choice of topics is guided by the underlying theme of modules as a basic unifying concept in mathematics. Beginning with standard topics in groups and ring theory, the authors then develop basic module theory, culminating in the fundamental structure theorem for finitely generated modules over a principal ideal domain. They then treat canonical form theory in linear algebra as an application of this fundamental theorem. Module theory is also used in investigating bilinear, sesquilinear, and quadratic forms. The authors develop some multilinear algebra (Hom and tensor product) and the theory of semisimple rings and modules and apply these results in the final chapter to study group represetations by viewing a representation of a group G over a field F as an F(G)-module. The book emphasizes proofs with a maximum of insight and a minimum of computation in order to promote understanding. However, extensive material on computation (for example, computation of canonical forms) is provided.

Détails de l'édition

• Éditeur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Date d'édition: 1999
• Langue: anglais
• ISBN 10: 3540978399
• ISBN 13: 9783540978398
• Reliure: Relié
• Nombre de pages: 536
• Coordonnées du fabricant: non disponible