Algebra

An Approach via Module Theory

William A. Adkins, Steven H. Weintraub

526 pages, parution le 01/01/1992

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Résumé

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.

Contents

Preface

Ch. 1 Groups 1
Ch. 2 Rings 49
Ch. 3 Modules and Vector Spaces 107
Ch. 4 Linear Algebra 182
Ch. 5 Matrices over PIDs 289
Ch. 6 Bilinear and Quadratic Forms 341
Ch. 7 Topics in Module Theory 395
Ch. 8 Group Representations 438

Appendix 507
Bibliography 510
Index of Notation 511
Index of Terminology

L'auteur - Steven H. Weintraub

Steven H. Weintraub is Professor and Chair of the Department of Mathematics at Lehigh University. This book, his fifth, grew out of a graduate course he taught at Lehigh. His other books include Algebra: An Approach via Module Theory (with W. A. Adkins).

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	William A. Adkins, Steven H. Weintraub
Parution	01/01/1992
Nb. de pages	526
Format	16 x 24
Couverture	Relié
Poids	946g
Intérieur	Noir et Blanc
EAN13	9780387978390
ISBN13	978-0-387-97839-0