Field extensions and galois theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. u.a.
Addison-Wesley u.a.
1984
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| Ausgabe: | 1. publ. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
22 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | LI, 294 S. |
| ISBN: | 0521302420 0201135213 |
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Datensatz im Suchindex
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| adam_text | Titel: Field extensions and Galois theory
Autor: Bastida, Julio R
Jahr: 1984
Contents Editor’s Statement......................................xiii Section Editor’s Foreword..................................xv Preface..................... xvii Historical Introduction...................................xxi Prerequisites..........................................xxv Notation..............................................xli Chapter 1 Preliminaries on Fields and Polynomials .............. 1 1.1 Fields of Fractions............................. 1 1.2 The Characteristic ............................. 5 1.3 Perfect Fields and Prime Fields....................10 1.4 Field Extensions...............................13 1.5 Factorization of Polynomials......................18 1.6 Splitting of Polynomials .........................29 1.7 Separable Polynomials ..........................34 Notes ......................................39 Chapter 2 Algebraic Extensions............................41 2.1 Algebraic Extensions............................41 2.2 Algebraically Closed Fields.......................56 2.3 Normal Extensions.............................64 2.4 Purely Inseparable Extensions.....................74 2.5 Separable Extensions ...........................80 Notes ......................................89 xi
Content xii Chapter 3 Galois Theory................................. 9 . 3.1 Some Vector Spaces of Mappings of Fields............ 9 . 3.2 The General Galois Correspondences................91 3.3 Galois Extensions..............................11 3.4 Finite Galois Theory............................121 3.5 Roots of Unity................................141 3.6 Primitive Elements.............................15 3.7 Separable and Inseparable Degrees..................151 3.8 Norms and Traces .............................16! 3.9 Cyclic Extensions..............................17* 3.10 Solvability by Radicals..........................18* 3.11 Finite Fields .................................18: 3.12 Infinite Galois Theory...........................19 Notes . .....................................20: Chapter 4 Transcendental Extensions........................21! 4.1 Dimensional Operators.................. 21: 4.2 Transcendence Bases and Transcendence Degree........21 4.3 Specializations and Places of Fields .................22 4.4 Separable Extensions ...........................24: 4.5 Derivations of Fields............................25 4.6 Derivations of Algebraic Function Fields .............27 Notes ......................................27 References and Selected Bibliography ........................28 Index...............................................29
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| discipline | Mathematik |
| edition | 1. publ. |
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| isbn | 0521302420 0201135213 |
| language | English |
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| physical | LI, 294 S. |
| publishDate | 1984 |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Bastida, Julio R. Verfasser aut Field extensions and galois theory Julio R. Bastida 1. publ. Reading, Mass. u.a. Addison-Wesley u.a. 1984 LI, 294 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 22 Extensions de corps (Mathématiques) Extensions de corps (mathématiques) ram Galois, Théorie de Galois, Théorie de ram Field extensions (Mathematics) Galois theory Körpererweiterung (DE-588)4164435-9 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Körpererweiterung (DE-588)4164435-9 s Galois-Theorie (DE-588)4155901-0 s DE-604 Encyclopedia of mathematics and its applications 22 (DE-604)BV000903719 22 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000171526&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bastida, Julio R. Field extensions and galois theory Encyclopedia of mathematics and its applications Extensions de corps (Mathématiques) Extensions de corps (mathématiques) ram Galois, Théorie de Galois, Théorie de ram Field extensions (Mathematics) Galois theory Körpererweiterung (DE-588)4164435-9 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4164435-9 (DE-588)4155901-0 |
| title | Field extensions and galois theory |
| title_auth | Field extensions and galois theory |
| title_exact_search | Field extensions and galois theory |
| title_full | Field extensions and galois theory Julio R. Bastida |
| title_fullStr | Field extensions and galois theory Julio R. Bastida |
| title_full_unstemmed | Field extensions and galois theory Julio R. Bastida |
| title_short | Field extensions and galois theory |
| title_sort | field extensions and galois theory |
| topic | Extensions de corps (Mathématiques) Extensions de corps (mathématiques) ram Galois, Théorie de Galois, Théorie de ram Field extensions (Mathematics) Galois theory Körpererweiterung (DE-588)4164435-9 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Extensions de corps (Mathématiques) Extensions de corps (mathématiques) Galois, Théorie de Field extensions (Mathematics) Galois theory Körpererweiterung Galois-Theorie |
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