Theory of General Division Rings
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Skew Fields by P. M. Cohn
Book DescriptionNon-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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Book DetailsISBN: 9780521432177
(228mm x 152mm x 29mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 28-Jul-1995
Country of Publication: United Kingdom
Books By Author P. M. Cohn
Lie Group, Paperback (January 2009)
The theory of Lie groups rests on three pillars: analysis, topology and algebra.
Skew Fields, Paperback (May 2008)
This work offers a comprehensive account of skew fields and related mathematics.
Free Ideal Rings and Localization in General Rings, Hardback (June 2006)
This book presents the theory of free ideal rings (firs) in detail.
Classic Algebra, Hardback (August 2000)» View all books by P. M. Cohn
Fundamental to all areas of mathematics, algebra provides the cornerstone for the student's development. The concepts are often intuitive, but some can take years of study to fully absorb. For over twenty years, the author's classic three-volume set, Algebra, has been regarded by many as the most outstanding introductory work available.
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