This book will be of interest to graduate students in pure mathematics and to professional mathematicians.
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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