Skew Fields : Theory of General Division Rings - P. M. Cohn

Skew Fields

Theory of General Division Rings

By: P. M. Cohn, Cohn P. M., G. -C Rota (Editor)

Hardcover | 2 October 1995

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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.
Industry Reviews
From reviews of the hardback: '... the first book on this theme and will be the basis of any future development in this field.' J. Schoissengeier, Monatshefte fur Mathematik From reviews of the hardback: 'While the material is quite technical, the book is very readable.' Mathematika From reviews of the hardback: '... an up-to-date account.' European Mathematical Society Newsletter From reviews of the hardback: 'This is a tremendous piece of work, whose importance will grow for many years.' Bulletin of the London Mathematic Society

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