000			02781nam a22003738i 4500
001			CR9781139087193
003			UkCbUP
005			20200124160235.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			110512s1995||||enk o ||1 0|eng|d
020			_a9781139087193 (ebook)
020			_z9780521432177 (hardback)
020			_z9780521062947 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA251.5 _b.C633 1995
082	0	0	_a512/.3 _220
100	1		_aCohn, P. M. _q(Paul Moritz), _eauthor.
245	1	0	_aSkew fields : _btheory of general division rings / _cP.M. Cohn.
264		1	_aCambridge : _bCambridge University Press, _c1995.
300			_a1 online resource (xv, 500 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aEncyclopedia of mathematics and its applications ; _vvolume 57
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aFrom the preface to Skew Field Constructions -- 1. Rings and their fields of fractions -- 2. Skew polynomial rings and power series rings -- 3. Finite skew field extensions and applications -- 4. Localization -- 5. Coproducts of fields -- 6. General skew fields -- 7. Rational relations and rational identities -- 8. Equations and singularities -- 9. Valuations and orderings on skew fields.
520			_aNon-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.
650		0	_aDivision rings.
650		0	_aAlgebraic fields.
776	0	8	_iPrint version: _z9780521432177
830		0	_aEncyclopedia of mathematics and its applications ; _vv. 57.
856	4	0	_uhttps://doi.org/10.1017/CBO9781139087193
999			_c518028 _d518026