Pub. Date:
Springer-Verlag New York, LLC
Algebra: An Approach Via Module Theory

Algebra: An Approach Via Module Theory


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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.

Product Details

ISBN-13: 9783540978398
Publisher: Springer-Verlag New York, LLC
Publication date: 09/01/1992
Series: Graduate Texts in Mathematics
Pages: 536
Product dimensions: 5.51(w) x 8.66(h) x (d)

Table of Contents

Groups.- Rings.- Modules and Vector Spaces.- Linear Algebra.- Matrices over PIDs.- Bilinear and Quadratic Forms.- Topics in Module Theory.- Group Representations.- Appendix.- Bibliography.- Index of Notation.- Index of Terminology.

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