CiNii 図書 - Skew fields

The book is written in three parts. Part I consists of preparatory work on algebras, needed in Parts II and III. This material is presented in a classical, though unusual, way. Part II consists of a modern description of the theory of Brauer groups over fields (from as elementary a point of view as possible). Part III covers some new developments in the theory which, until now, have not been available except in journals. The principal topic discussed in this section is reduced K,-theory. This book will be of interest to graduate students in pure mathematics and to professional mathematicians.

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 Dieudonne 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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