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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

Tabla de contenidos provista por Syndetics

• 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