抽象代數(shù)講義（第3卷）

內(nèi)容概要

　　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.

書籍目錄

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……

編輯推薦

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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