Skew fields: theory of general division rings
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York
Cambridge University Press
1995
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
v. 57 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and indexes 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 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 |
| Beschreibung: | 1 Online-Ressource (xv, 500 p.) |
| ISBN: | 0521432170 1107088402 9780521432177 9781107088405 |
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| 500 | |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 | ||
| 500 | |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 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 | ||
| 500 | |a 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 | ||
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Datensatz im Suchindex
| _version_ | 1804175492522180608 |
|---|---|
| any_adam_object | |
| author | Cohn, P. M., (Paul Moritz) |
| author_facet | Cohn, P. M., (Paul Moritz) |
| author_role | aut |
| author_sort | Cohn, P. M., (Paul Moritz) |
| author_variant | p m p m c pmpm pmpmc |
| building | Verbundindex |
| bvnumber | BV043091296 |
| collection | ZDB-4-EBA |
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| 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 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:09Z |
| institution | BVB |
| isbn | 0521432170 1107088402 9780521432177 9781107088405 |
| language | English |
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| spelling | Cohn, P. M., (Paul Moritz) Verfasser aut Skew fields theory of general division rings P.M. Cohn New York Cambridge University Press 1995 1 Online-Ressource (xv, 500 p.) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications v. 57 Includes bibliographical references and indexes 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 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 Corps gauches ram Corps algébriques ram Lichamen (wiskunde) gtt Ringen (wiskunde) gtt Corps gauches Corps algébriques MATHEMATICS / Algebra / Intermediate bisacsh Algebraic fields fast Division rings fast Division rings Algebraic fields Schiefkörper (DE-588)4052359-7 gnd rswk-swf Schiefkörper (DE-588)4052359-7 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=569375 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cohn, P. M., (Paul Moritz) Skew fields theory of general division rings Corps gauches ram Corps algébriques ram Lichamen (wiskunde) gtt Ringen (wiskunde) gtt Corps gauches Corps algébriques MATHEMATICS / Algebra / Intermediate bisacsh Algebraic fields fast Division rings fast 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 | Corps gauches ram Corps algébriques ram Lichamen (wiskunde) gtt Ringen (wiskunde) gtt Corps gauches Corps algébriques MATHEMATICS / Algebra / Intermediate bisacsh Algebraic fields fast Division rings fast Division rings Algebraic fields Schiefkörper (DE-588)4052359-7 gnd |
| topic_facet | Corps gauches Corps algébriques Lichamen (wiskunde) Ringen (wiskunde) MATHEMATICS / Algebra / Intermediate Algebraic fields Division rings Schiefkörper |
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