Skew Fields: Theory of General Division Rings Hardcover - 1995
by P. M. Cohn
From the rear cover
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 are 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 theorems 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. 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. The treatment of equations over skew fields has been simplified and extended by the use of matrix methods, and the beginnings of non-commutative algebraic geometry are presented, with a precise account of the problems that need to be overcome for a satisfactory theory. A separate chapter describes valuations and orderings on skew fields, with a construction applicable to free fields. Numerous exercises test the reader's understanding, presenting further aspects and open problems in concise form, and notes and comments at the ends of chapters provide historical background.
Details
- Title Skew Fields: Theory of General Division Rings
- Author P. M. Cohn
- Binding Hardcover
- Pages 520
- Volumes 1
- Language ENG
- Publisher Cambridge University Press
- Date 1995-07-28
- ISBN 9780521432177 / 0521432170
- Weight 1.9 lbs (0.86 kg)
- Dimensions 9.49 x 6.44 x 1.26 in (24.10 x 16.36 x 3.20 cm)
- Library of Congress subjects Algebraic fields, Division rings
- Library of Congress Catalog Number 95020221
- Dewey Decimal Code 512.3
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Skew Fields: Theory of General Division Rings: Vol 57
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Skew Fields: Theory of General Division Rings (Encyclopedia of Mathematics and its Applications, Series Number 57)
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