抽象代数讲义·第3卷（英文版）

The present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II.

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The present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II.

　　此书为英文版！

INTRODUCTION
1. Extension of homomorphisms
2. Algebras
3. Tensor products of vector spaces
4. Tensor product of algebras
CHAPTER I: FINITE DIMENSIONAL EXTENSION FIELDS
1. Some vector spaces associated with mappings of fields
2. The Jacobson-Bourbaki correspondence
3. Dedekind independence theorem for isomorphisms of a field
4. Finite groups of automorphisms
5. Splitting field of a polynomial
6. Multiple roots. Separable polynomials
7. The "fundamental theorem" of Galois theory
8. Normal extensions. Normal closures
9. Structure of algebraic extensions. Separability
10. Degrees of separability and inseparability. Structure of normal extensions
11. Primitive elements
12. Normal bases
13. Finite fields

The present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II. In preparing this book we have had a. number of objectives in mind. First and foremost has been that of presenting the b..