Foreword Groups Rings Modules Polynomials Algebraic Equations Galois Theory Extensions of Rings Transcendental Extensions Algebraic Spaces Noetherian Rings and Modules Real Fields Absolute Values Matrices and Linear Maps Representation of One Endomorphism Structure of Bilinear Forms The Tensor Product Semisimplicity Representations of Finite Groups The Alternating Product General Homology Theory Finite Free Resolutions Appendices Bibliography
Foreword * Groups * Rings * Modules * Polynomials * Algebraic Equations * Galois Theory * Extensions of Rings * Transcendental Extensions * Algebraic Spaces * Noetherian Rings and Modules * Real Fields * Absolute Values * Matrices and Linear Maps * Representation of One Endomorphism * Structure of Bilinear Forms * The Tensor Product * Semisimplicity * Representations of Finite Groups * The Alternating Product * General Homology Theory * Finite Free Resolutions * Appendices * Bibliography
This book is intended as a basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text.