Skew Fields
eBook - PDF

Skew Fields

Theory of General Division Rings

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Skew Fields

Theory of General Division Rings

Book details
Table of contents
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About This Book

Non-commutative fields (also called skew fields or division rings) have not been studied as thoroughly as their commutative counterparts, and most accounts have hitherto been confined to division algebras - that is skew fields finite dimensional over their centre. Based on the author's LMS lecture note volume Skew Field Constructions, the present work offers a comprehensive account of skew fields. The axiomatic foundation, and a precise description of the embedding problem, is followed by an account of algebraic and topological construction methods, in particular, the author's general embedding theory is presented with full proofs, leading to the construction of skew fields. The powerful coproduct theorem of G. M. Bergman is proved here, as well as the properties of the matrix reduction functor, a useful but little-known construction providing a source of examples and counter-examples. The construction and basic properties of existentially closed skew fields are given, leading to an example of a model class with an infinite forcing companion which is not axiomatizable.

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Information

Publisher
Cambridge University Press
Year
1995
ISBN
9781139106542
Topic
Mathematics
Subtopic
Algebra
Index
Mathematics

Table of contents

  1. Cover
  2. Half Title
  3. Series Page
  4. Title
  5. Copyright
  6. Dedication
  7. PREFACE
  8. NOTE TO THE READER
  9. PROLOGUE
  10. 1 Rings and their fields of fractions
  11. 2 Skew polynomial rings and power series rings
  12. 3 Finite skew field extensions and applications
  13. 4 Localization
  14. 5 Coproducts of fields
  15. 6 General skew fields
  16. 7 Rational relations and rational identities
  17. 8 Equations and singularities
  18. 9 Valuations and orderings on skew fields
  19. STANDARD NOTATIONS
  20. LIST OF SPECIAL NOTATIONS USED THROUGHOUT THE TEXT
  21. BIBLIOGRAPHY AND AUTHOR INDEX
  22. SUBJECT INDEX