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Skew Fields

£39.99

Part of London Mathematical Society Lecture Note Series

  • Date Published: February 1983
  • availability: Available
  • format: Paperback
  • isbn: 9780521272742

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  • 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.

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    Product details

    • Date Published: February 1983
    • format: Paperback
    • isbn: 9780521272742
    • length: 196 pages
    • dimensions: 229 x 152 x 11 mm
    • weight: 0.3kg
    • availability: Available
  • 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.

  • Author

    P. K. Draxl

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