Skew Fields: Theory of General Division Rings: 57 (Encyclopedia of Mathematics and its Applications) Book + PRICE WATCH * Amazon pricing is not included in price watch

Skew Fields: Theory of General Division Rings: 57 (Encyclopedia of Mathematics and its Applications) Book

Based on the authors 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 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.Read More

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  • Product Description

    Algebraists have studied noncommutative fields (also called skew fields or division rings) less thoroughly than their commutative counterparts. Most existing accounts have been confined to division algebras, i.e. skew fields that are finite dimensional over their center. This work offers the first comprehensive account of skew fields. It is based on the author's LMS Lecture Note Volume "Skew Field Constructions". The axiomatic foundation and a precise description of the embedding problem precedes an account of algebraic and topological construction methods. The author presents his general embedding theory with full proofs, leading to the construction of skew fields. The author has simplified his treatment of equations over skew fields and has extended it by the use of matrix methods. 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. Notes and comments at the end of chapters provide historical background. The book will appeal to researchers in algebra, logic, and algebraic geometry, as well as graduate students in these fields.

  • 0521432170
  • 9780521432177
  • P. M. Cohn FRS
  • 28 July 1995
  • Cambridge University Press
  • Hardcover (Book)
  • 520
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