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This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules.
"In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."--A. Rosenberg, "Mathematical Reviews"
List of contents
Preface Pt. I: Fields 1: Field extensions 2: Ruler and compass constructions 3: Foundations of Galois theory 4: Normality and stability 5: Splitting fields 6: Radical extensions 7: The trace and norm theorems 8: Finite fields 9: Simple extensions 10: Cubic and quartic equations 11: Separability 12: Miscellaneous results on radical extensions 13: Infinite algebraic extensions Pt. II: Rings 1: The radical 2: Primitive rings and the density theorem 3: Semi-simple rings 4: The Wedderburn principal theorem 5: Theorems of Hopkins and Levitzki 6: Primitive rings with minimal ideals and dual vector spaces 7: Simple rings Pt. III: Homological Dimension 1: Dimension of modules 2: Global dimension 3: First theorem on change of rings 4: Polynomial rings 5: Second theorem on change of rings 6: Third theorem on change of rings 7: Localization 8: Preliminary lemmas 9: A regular ring has finite global dimension 10: A local ring of finite global dimension is regular 11: Injective modules 12: The group of homomorphisms 13: The vanishing of Ext 14: Injective dimension Notes Index
About the author
Irving Kaplansky is Director Emeritus of the Mathematical Sciences Research Institute and George Herbert Mead Distinguished Service Professor Emeritus in the Department of Mathematics at the University of Chicago.
Summary
This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules.
