Fields and Rings

Description

Title page PREFACE Part 1. FIELDS Introduction 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 Part II. RINGS Introduction 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 (1) The enveloping ring and the centroid (2) Tensor products (3) Maximal subfields (4) Polynomial identities (5) Extension of isomorphisms Part III. HOMOLOGICAL DIMENSION Introduction 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 INDEX Notes from the 2nd edition