Skew fields: theory of general division rings
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 lect...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1995
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 57 |
| Links: | https://doi.org/10.1017/CBO9781139087193 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (xv, 500 Seiten) |
| ISBN: | 9781139087193 |
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| 520 | |a 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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| spelling | Cohn, P. M. Skew fields theory of general division rings P.M. Cohn Cambridge Cambridge University Press 1995 1 Online-Ressource (xv, 500 Seiten) txt c cr Encyclopedia of mathematics and its applications volume 57 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. Erscheint auch als Druck-Ausgabe 9780521062947 Erscheint auch als Druck-Ausgabe 9780521432177 |
| spellingShingle | Cohn, P. M. Skew fields theory of general division rings |
| title | Skew fields theory of general division rings |
| title_auth | Skew fields theory of general division rings |
| title_exact_search | Skew fields theory of general division rings |
| title_full | Skew fields theory of general division rings P.M. Cohn |
| title_fullStr | Skew fields theory of general division rings P.M. Cohn |
| title_full_unstemmed | Skew fields theory of general division rings P.M. Cohn |
| title_short | Skew fields |
| title_sort | skew fields theory of general division rings |
| title_sub | theory of general division rings |
| work_keys_str_mv | AT cohnpm skewfieldstheoryofgeneraldivisionrings |