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Fields and rings

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Author(s): Irving Kaplansky
Series: Chicago Lectures in Mathematics
Edition: 2
Publisher: The University of Chicago Press
Year: 1972

Language: English
City: Chicago

Title
Contents
Preface to the second edition
Preface to the first edition
Part 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
Part 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
Part 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 local 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
Bibliography for the notes
Index