Author(s): Irving Kaplansky
Publisher: Chicago
Year: 1969
Language: English
Commentary: First edition + added the new material from the second
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
