Skew Fields Theory of General Division Rings [Paperback]

This work offers a comprehensive account of skew fields and related mathematics.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.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.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 arl³