Skew Fields: Theory of General Division Rings

Skew Fields: Theory of General Division Rings

by P. M. Cohn
     
 

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ISBN-10: 0521062942

ISBN-13: 9780521062947

Pub. Date: 05/15/2008

Publisher: Cambridge University Press

Based on the authors LMS lecture note volume , 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

Overview

Based on the authors LMS lecture note volume , 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 are 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.Numerous exercises test the readers understanding, presenting further aspects and open problems in concise form, and notes and comments at the end of chapters provide historical background.

Product Details

ISBN-13:
9780521062947
Publisher:
Cambridge University Press
Publication date:
05/15/2008
Series:
Encyclopedia of Mathematics and its Applications Series, #57
Edition description:
New Edition
Pages:
520
Product dimensions:
6.10(w) x 9.20(h) x 1.20(d)

Table of Contents

Preface; From the preface to Skew Field Constructions; Note to the reader; Prologue; 1. Rings and their fields of fractions; 2. Skew polynomial rings and power series rings; 3. Finite skew field extensions and applications; 4. Localization; 5. Coproducts of fields; 6. General skew fields; 7. Rational relations and rational identities; 8. Equations and singularities; 9. Valuations and orderings on skew fields; Standard notations; List of special notations used throughout the text; Bibliography and author index; Subject index.

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