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:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1995
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| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 57 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xv, 500 pages) |
| ISBN: | 9781139087193 |
| DOI: | 10.1017/CBO9781139087193 |
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| 505 | 8 | |a From 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 | |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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| author | Cohn, P. M. |
| author_facet | Cohn, P. M. |
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| author_sort | Cohn, P. M. |
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| contents | From 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 |
| ctrlnum | (ZDB-20-CBO)CR9781139087193 (OCoLC)967679472 (DE-599)BVBBV043941856 |
| dewey-full | 512/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.3 |
| dewey-search | 512/.3 |
| dewey-sort | 3512 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139087193 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781139087193 |
| language | English |
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| spelling | Cohn, P. M. Verfasser aut Skew fields theory of general division rings P.M. Cohn Cambridge Cambridge University Press 1995 1 online resource (xv, 500 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 57 Title from publisher's bibliographic system (viewed on 05 Oct 2015) From 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 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 Division rings Algebraic fields Schiefkörper (DE-588)4052359-7 gnd rswk-swf Schiefkörper (DE-588)4052359-7 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-06294-7 Erscheint auch als Druckausgabe 978-0-521-43217-7 https://doi.org/10.1017/CBO9781139087193 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cohn, P. M. Skew fields theory of general division rings From 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 Division rings Algebraic fields Schiefkörper (DE-588)4052359-7 gnd |
| subject_GND | (DE-588)4052359-7 |
| 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 |
| topic | Division rings Algebraic fields Schiefkörper (DE-588)4052359-7 gnd |
| topic_facet | Division rings Algebraic fields Schiefkörper |
| url | https://doi.org/10.1017/CBO9781139087193 |
| work_keys_str_mv | AT cohnpm skewfieldstheoryofgeneraldivisionrings |