Articles liés à Skew Fields: Theory of General Division Rings
Synopsis
Non-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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Présentation de l'éditeur
Non-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.
Revue de presse
Review of the hardback: '... the first book on this theme and will be the basis of any future development in this field.' J. Schoissengeier, Monatshefte für Mathematik
Review of the hardback: 'While the material is quite technical, the book is very readable.' Mathematika
Review of the hardback: '... an up-to-date account.' European Mathematical Society Newsletter
Review 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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Skew fields: Theory of general division rings
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Cambridge University Press, 1995
ISBN 10 : 0521432170
ISBN 13 : 9780521432177
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Hardcover. Etat : ex library-very good. Encyclopedia of Mathematics Vol. 57. xv, 500 p. 24 cm. Red cloth. Ex library with labels on spine and front cover, ink stamps on top edge, rear free endpaper, and first pages. Spine a bit faded. N° de réf. du vendeur 148621
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Skew Fields : Theory of General Division Rings
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Cambridge University Press, 2003
ISBN 10 : 0521432170
ISBN 13 : 9780521432177
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Couverture rigide
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Skew Fields : Theory Of General Division Rings
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Cambridge University Press, 1995
ISBN 10 : 0521432170
ISBN 13 : 9780521432177
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Skew Fields: Theory of General Division Rings (Encyclopedia of Mathematics and its Applications, Series Number 57)
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Cambridge University Press, 1995
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ISBN 13 : 9780521432177
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Skew Fields: Theory of General Division Rings (Encyclopedia of Mathematics and its Applications, Series Number 57)
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Cambridge University Press, 1995
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ISBN 13 : 9780521432177
Neuf
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Skew Fields: Theory of General Division Rings (Encyclopedia of Mathematics and its Applications, Series Number 57)
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ISBN 13 : 9780521432177
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Skew Fields: Theory of General Division Rings (Encyclopedia of Mathematics and its Applications, Series Number 57)
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ISBN 13 : 9780521432177
Neuf
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Skew Fields
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Cambridge University Press, 2003
ISBN 10 : 0521432170
ISBN 13 : 9780521432177
Neuf
Couverture rigide
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Gebunden. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Based on the author s LMS lecture note volume Skew Field Constructions, the present work offers a comprehensive account of skew fields. Numerous exercises test the reader s understanding, presenting further aspects and open problems in a concise form. The n. N° de réf. du vendeur 446935336
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Skew Fields: Theory of General Division Rings: Vol 57
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Cambridge Univ Pr, 1995
ISBN 10 : 0521432170
ISBN 13 : 9780521432177
Neuf
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Hardcover. Etat : Brand New. 516 pages. 9.75x6.75x1.25 inches. In Stock. This item is printed on demand. N° de réf. du vendeur __0521432170
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Skew Fields: Theory of General Division Rings (Hardcover)
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Cambridge University Press, Cambridge, 2003
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ISBN 13 : 9780521432177
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Hardcover. Etat : new. Hardcover. 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. Non-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 are 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 theorems 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. 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. The treatment of equations over skew fields has been simplified and extended by the use of matrix methods, and the beginnings of non-commutative algebraic geometry are presented, with a precise account of the problems that need to be overcome for a satisfactory theory. 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, and notes and comments at the ends of chapters provide historical background. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. N° de réf. du vendeur 9780521432177
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