Algebra: An Approach Via Module Theory: v. 136 (Graduate Texts in Mathematics) - Hardcover

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.