Skew Fields

Table of Contents

Preface
Conventions on terminology
Part I. Skew Fields and Simple Rings:
1. Some ad hoc results on skew fields
2. Rings of matrices over skew fields
3. Simple rings and Wedderburn's main theorem
4. A short cut to tensor products
5. Tensor products and algebras
6. Tensor products and Galois theory
7. Skolem-Noether theorem and Centralizer theorem
8. The corestriction of algebras
Part II. Skew Fields and Brauer Groups:
9. Brauer groups over fields
10. Cyclic algebras
11. Power norm residue algebras
12. Brauer groups and Galois cohomology
13. The formalism of crossed products
14. Quaternion algebras
15. p-Algebras
16. Skew fields with involution
17. Brauer groups and K2-theory of fields
18. A survey of some further results
Part III. Reduced K1-Theory of Skew Fields:
19. The Bruhat normal form
20. The Dieudonné determinant
21. The structure of SLn (D) for n ≥ 2
22. Reduced norms and traces
23. The reduced Whitehead group SK1 (D) and Wang's theorem
24. SK1 (D) ≠ 1 for suitable D
Remarks on USK1 (D,I)
Bibliography
Thesaurus
Index.

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• Front Matter (429 KB)
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• Marketing Excerpt (563 KB)
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