Skew Fields Book

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 Dieudonnà determinant;
21. The structure of SLn (D) for n âe¥ 2;
22. Reduced norms and traces;
23. The reduced Whitehead group SK1 (D) and Wang's theorem;
24. SK1 (D) âe  1 for suitable D; Remarks on USK1 (D,I); Bibliography; Thesaurus; Index.