抽象代数讲义（第3卷）
2000-12
世界图书出版公司
Nathan Jacobson
217
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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.
INTRODUCTIONSECTION1. Extension of homomorphisms2. Algebras3. Tensor products of vector spaces4. Tensor product of algebrasCHAPTER I￡oFINITE DIMENSIONAL EXTENSION FIELDS1. Some vector spaces associated with mappings of fields2. The Jacobson-Bourbaki correspondence3. Dedekind independence theorem for isomorphisms of a field4. Finite groups of automorphisms5. Splitting field of a polynomial6. Multiple roots. Separable polynomials7. The "fundamental theorem" of Galois theory8. Normal extensions. Normal closures9. Structure of algebraic extensions. Separability10. Degrees of separability and inseparability. Structure of normal extensions11. Primitive elements12. Normal bases13. Finite fields14. Regular representation, trace and norm15. Galois cohomology16. Composites of fieldsCHAPTER II￡oGALOIS THEORY OF EQUATIONS1. The Galois group of an equation2. Pure equations3. Galois' criterion for solvability by radicals……
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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这是代数学方面的一本经典著作，据闻作者曾任美国数学会的历时长。三卷本的《抽象代数讲义》和两卷本的《基础代数学》内容都差不多，不过后者的名气在国内远远胜过前者，只是国内目前很难找到那本书，一些特殊情况才能够找到后者的中译本。这样，前者可以说是一个极好的替代品。