Field extensions and Galois theory /:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [Cambridgeshire] ; New York, NY, USA :
Cambridge University Press,
©1984.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 22. Encyclopedia of mathematics and its applications. Section, Algebra. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Publication taken over by Cambridge University Press in 1984. |
| Beschreibung: | 1 online resource (li, 294 pages) : illustrations |
| Bibliographie: | Imprint and ISBN from label on title pages verso. Imprint on t.p. : Reading, Mass.: Addison-Wesley, Advanced Book Program, 1984. Includes bibliographical references (pages 281-290) and index. |
| ISBN: | 9781107266766 1107266769 |
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| 505 | 0 | |a Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Editor's Statement; Foreword; Preface; Historical Introduction; Prerequisites; Notation; NOTATION PERTAINING TO THE THEORY OF FIELD EXTENSIONS AND GALOIS THEORY; Chapter 1 Preliminaries on Fields and Polynomials; 1.1. FIELDS OF FRACTIONS; PROBLEMS; 1.2. THE CHARACTERISTIC; 1.2.1. Examples; PROBLEMS; 1.3. PERFECT FIELDS AND PRIME FIELDS; PROBLEMS; 1.4. FIELD EXTENSIONS; 1.4.1. Examples; PROBLEMS; 1.5. FACTORIZATION OF POLYNOMIALS; 1.5.10. Examples; PROBLEMS; 1.6. SPLITTING OF POLYNOMIALS; 1.6.1. Examples; 1.6.2. Examples | |
| 505 | 8 | |a 1.6.6. ExamplesPROBLEMS; 1.7. SEPARABLE POLYNOMIALS; 1.7.4. Examples; PROBLEMS; NOTES; Chapter 2 Algebraic Extensions; 2.1. ALGEBRAIC EXTENSIONS; 2.1.1. Examples; 2.1.7. Examples; PROBLEMS; 2.2. ALGEBRAICALLY CLOSED FIELDS; 2.2.8. Examples; PROBLEMS; 2.3. NORMAL EXTENSIONS; 2.3.1. Examples; 2.3.16. Examples; PROBLEMS; 2.4. PURELY INSEPARABLE EXTENSIONS; PROBLEMS; 2.5. SEPARABLE EXTENSIONS; PROBLEMS; NOTES; Chapter 3 Galois Theory; 3.1. SOME VECTOR SPACES OF MAPPINGS OF FIELDS; 3.1.4. Examples; PROBLEMS; 3.2. THE GENERAL GALOIS CORRESPONDENCES; 3.2.4. Examples; PROBLEMS; 3.3. GALOIS EXTENSIONS | |
| 505 | 8 | |a PROBLEMS3.4. FINITE GALOIS THEORY; PROBLEMS; 3.5. ROOTS OF UNITY; PROBLEMS; 3.6. PRIMITIVE ELEMENTS; PROBLEMS; 3.7. SEPARABLE AND INSEPARABLE DEGREES; PROBLEMS; 3.8. NORMS AND TRACES; 3.8.1. Examples; PROBLEMS; 3.9. CYCLIC EXTENSIONS; PROBLEMS; 3.10. SOLVABILITY BY RADICALS; PROBLEMS; 3.11. FINITE FIELDS; 3.11.4. Examples; PROBLEMS; 3.12. INFINITE GALOIS THEORY; PROBLEMS; NOTES; Suggestions for further reading; Chapter 4 Transcendental Extensions; 4.1. DIMENSIONAL OPERATORS; 4.1.1. Examples; 4.1.2. Examples; PROBLEMS; 4.2. TRANSCENDENCE BASES AND TRANSCENDENCE DEGREE; PROBLEMS | |
| 505 | 8 | |a 4.3. SPECIALIZATIONS AND PLACES OF FIELDS4.3.1. Examples; PROBLEMS; 4.4. SEPARABLE EXTENSIONS; PROBLEMS; 4.5. DERIVATIONS OF FIELDS; 4.5.1. Examples; 4.5.5. Examples; PROBLEMS; 4.6. DERIVATIONS OF ALGEBRAIC FUNCTION FIELDS; PROBLEMS; NOTES; Suggestions for further reading; References and Selected Bibliography; Bibliography; Of historical interest; Index | |
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| contents | Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Editor's Statement; Foreword; Preface; Historical Introduction; Prerequisites; Notation; NOTATION PERTAINING TO THE THEORY OF FIELD EXTENSIONS AND GALOIS THEORY; Chapter 1 Preliminaries on Fields and Polynomials; 1.1. FIELDS OF FRACTIONS; PROBLEMS; 1.2. THE CHARACTERISTIC; 1.2.1. Examples; PROBLEMS; 1.3. PERFECT FIELDS AND PRIME FIELDS; PROBLEMS; 1.4. FIELD EXTENSIONS; 1.4.1. Examples; PROBLEMS; 1.5. FACTORIZATION OF POLYNOMIALS; 1.5.10. Examples; PROBLEMS; 1.6. SPLITTING OF POLYNOMIALS; 1.6.1. Examples; 1.6.2. Examples 1.6.6. ExamplesPROBLEMS; 1.7. SEPARABLE POLYNOMIALS; 1.7.4. Examples; PROBLEMS; NOTES; Chapter 2 Algebraic Extensions; 2.1. ALGEBRAIC EXTENSIONS; 2.1.1. Examples; 2.1.7. Examples; PROBLEMS; 2.2. ALGEBRAICALLY CLOSED FIELDS; 2.2.8. Examples; PROBLEMS; 2.3. NORMAL EXTENSIONS; 2.3.1. Examples; 2.3.16. Examples; PROBLEMS; 2.4. PURELY INSEPARABLE EXTENSIONS; PROBLEMS; 2.5. SEPARABLE EXTENSIONS; PROBLEMS; NOTES; Chapter 3 Galois Theory; 3.1. SOME VECTOR SPACES OF MAPPINGS OF FIELDS; 3.1.4. Examples; PROBLEMS; 3.2. THE GENERAL GALOIS CORRESPONDENCES; 3.2.4. Examples; PROBLEMS; 3.3. GALOIS EXTENSIONS PROBLEMS3.4. FINITE GALOIS THEORY; PROBLEMS; 3.5. ROOTS OF UNITY; PROBLEMS; 3.6. PRIMITIVE ELEMENTS; PROBLEMS; 3.7. SEPARABLE AND INSEPARABLE DEGREES; PROBLEMS; 3.8. NORMS AND TRACES; 3.8.1. Examples; PROBLEMS; 3.9. CYCLIC EXTENSIONS; PROBLEMS; 3.10. SOLVABILITY BY RADICALS; PROBLEMS; 3.11. FINITE FIELDS; 3.11.4. Examples; PROBLEMS; 3.12. INFINITE GALOIS THEORY; PROBLEMS; NOTES; Suggestions for further reading; Chapter 4 Transcendental Extensions; 4.1. DIMENSIONAL OPERATORS; 4.1.1. Examples; 4.1.2. Examples; PROBLEMS; 4.2. TRANSCENDENCE BASES AND TRANSCENDENCE DEGREE; PROBLEMS 4.3. SPECIALIZATIONS AND PLACES OF FIELDS4.3.1. Examples; PROBLEMS; 4.4. SEPARABLE EXTENSIONS; PROBLEMS; 4.5. DERIVATIONS OF FIELDS; 4.5.1. Examples; 4.5.5. Examples; PROBLEMS; 4.6. DERIVATIONS OF ALGEBRAIC FUNCTION FIELDS; PROBLEMS; NOTES; Suggestions for further reading; References and Selected Bibliography; Bibliography; Of historical interest; Index |
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| indexdate | 2024-11-27T13:25:26Z |
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| series | Encyclopedia of mathematics and its applications ; Encyclopedia of mathematics and its applications. Section, Algebra. |
| series2 | Encyclopedia of mathematics and its applications ; Section, Algebra |
| spelling | Bastida, Julio R. Field extensions and Galois theory / Julio R. Bastida ; with a foreword by Roger Lyndon. Cambridge [Cambridgeshire] ; New York, NY, USA : Cambridge University Press, ©1984. 1 online resource (li, 294 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 22. Section, Algebra Imprint and ISBN from label on title pages verso. Imprint on t.p. : Reading, Mass.: Addison-Wesley, Advanced Book Program, 1984. Publication taken over by Cambridge University Press in 1984. Includes bibliographical references (pages 281-290) and index. Print version record. Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Editor's Statement; Foreword; Preface; Historical Introduction; Prerequisites; Notation; NOTATION PERTAINING TO THE THEORY OF FIELD EXTENSIONS AND GALOIS THEORY; Chapter 1 Preliminaries on Fields and Polynomials; 1.1. FIELDS OF FRACTIONS; PROBLEMS; 1.2. THE CHARACTERISTIC; 1.2.1. Examples; PROBLEMS; 1.3. PERFECT FIELDS AND PRIME FIELDS; PROBLEMS; 1.4. FIELD EXTENSIONS; 1.4.1. Examples; PROBLEMS; 1.5. FACTORIZATION OF POLYNOMIALS; 1.5.10. Examples; PROBLEMS; 1.6. SPLITTING OF POLYNOMIALS; 1.6.1. Examples; 1.6.2. Examples 1.6.6. ExamplesPROBLEMS; 1.7. SEPARABLE POLYNOMIALS; 1.7.4. Examples; PROBLEMS; NOTES; Chapter 2 Algebraic Extensions; 2.1. ALGEBRAIC EXTENSIONS; 2.1.1. Examples; 2.1.7. Examples; PROBLEMS; 2.2. ALGEBRAICALLY CLOSED FIELDS; 2.2.8. Examples; PROBLEMS; 2.3. NORMAL EXTENSIONS; 2.3.1. Examples; 2.3.16. Examples; PROBLEMS; 2.4. PURELY INSEPARABLE EXTENSIONS; PROBLEMS; 2.5. SEPARABLE EXTENSIONS; PROBLEMS; NOTES; Chapter 3 Galois Theory; 3.1. SOME VECTOR SPACES OF MAPPINGS OF FIELDS; 3.1.4. Examples; PROBLEMS; 3.2. THE GENERAL GALOIS CORRESPONDENCES; 3.2.4. Examples; PROBLEMS; 3.3. GALOIS EXTENSIONS PROBLEMS3.4. FINITE GALOIS THEORY; PROBLEMS; 3.5. ROOTS OF UNITY; PROBLEMS; 3.6. PRIMITIVE ELEMENTS; PROBLEMS; 3.7. SEPARABLE AND INSEPARABLE DEGREES; PROBLEMS; 3.8. NORMS AND TRACES; 3.8.1. Examples; PROBLEMS; 3.9. CYCLIC EXTENSIONS; PROBLEMS; 3.10. SOLVABILITY BY RADICALS; PROBLEMS; 3.11. FINITE FIELDS; 3.11.4. Examples; PROBLEMS; 3.12. INFINITE GALOIS THEORY; PROBLEMS; NOTES; Suggestions for further reading; Chapter 4 Transcendental Extensions; 4.1. DIMENSIONAL OPERATORS; 4.1.1. Examples; 4.1.2. Examples; PROBLEMS; 4.2. TRANSCENDENCE BASES AND TRANSCENDENCE DEGREE; PROBLEMS 4.3. SPECIALIZATIONS AND PLACES OF FIELDS4.3.1. Examples; PROBLEMS; 4.4. SEPARABLE EXTENSIONS; PROBLEMS; 4.5. DERIVATIONS OF FIELDS; 4.5.1. Examples; 4.5.5. Examples; PROBLEMS; 4.6. DERIVATIONS OF ALGEBRAIC FUNCTION FIELDS; PROBLEMS; NOTES; Suggestions for further reading; References and Selected Bibliography; Bibliography; Of historical interest; Index Field extensions (Mathematics) http://id.loc.gov/authorities/subjects/sh85048103 Galois theory. http://id.loc.gov/authorities/subjects/sh85052872 Extensions de corps (Mathématiques) Théorie de Galois. MATHEMATICS Algebra Intermediate. bisacsh Field extensions (Mathematics) fast Galois theory fast Galois-Theorie gnd http://d-nb.info/gnd/4155901-0 Körpererweiterung gnd http://d-nb.info/gnd/4164435-9 Galois, Théorie de. ram Print version: Bastida, Julio R. Field extensions and Galois theory. Cambridge [Cambridgeshire] ; New York, NY, USA : Cambridge University Press, ©1984 0521302420 (DLC) 85121629 (OCoLC)12050591 Encyclopedia of mathematics and its applications ; v. 22. http://id.loc.gov/authorities/names/n42010632 Encyclopedia of mathematics and its applications. Section, Algebra. http://id.loc.gov/authorities/names/n42035717 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=589162 Volltext |
| spellingShingle | Bastida, Julio R. Field extensions and Galois theory / Encyclopedia of mathematics and its applications ; Encyclopedia of mathematics and its applications. Section, Algebra. Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Editor's Statement; Foreword; Preface; Historical Introduction; Prerequisites; Notation; NOTATION PERTAINING TO THE THEORY OF FIELD EXTENSIONS AND GALOIS THEORY; Chapter 1 Preliminaries on Fields and Polynomials; 1.1. FIELDS OF FRACTIONS; PROBLEMS; 1.2. THE CHARACTERISTIC; 1.2.1. Examples; PROBLEMS; 1.3. PERFECT FIELDS AND PRIME FIELDS; PROBLEMS; 1.4. FIELD EXTENSIONS; 1.4.1. Examples; PROBLEMS; 1.5. FACTORIZATION OF POLYNOMIALS; 1.5.10. Examples; PROBLEMS; 1.6. SPLITTING OF POLYNOMIALS; 1.6.1. Examples; 1.6.2. Examples 1.6.6. ExamplesPROBLEMS; 1.7. SEPARABLE POLYNOMIALS; 1.7.4. Examples; PROBLEMS; NOTES; Chapter 2 Algebraic Extensions; 2.1. ALGEBRAIC EXTENSIONS; 2.1.1. Examples; 2.1.7. Examples; PROBLEMS; 2.2. ALGEBRAICALLY CLOSED FIELDS; 2.2.8. Examples; PROBLEMS; 2.3. NORMAL EXTENSIONS; 2.3.1. Examples; 2.3.16. Examples; PROBLEMS; 2.4. PURELY INSEPARABLE EXTENSIONS; PROBLEMS; 2.5. SEPARABLE EXTENSIONS; PROBLEMS; NOTES; Chapter 3 Galois Theory; 3.1. SOME VECTOR SPACES OF MAPPINGS OF FIELDS; 3.1.4. Examples; PROBLEMS; 3.2. THE GENERAL GALOIS CORRESPONDENCES; 3.2.4. Examples; PROBLEMS; 3.3. GALOIS EXTENSIONS PROBLEMS3.4. FINITE GALOIS THEORY; PROBLEMS; 3.5. ROOTS OF UNITY; PROBLEMS; 3.6. PRIMITIVE ELEMENTS; PROBLEMS; 3.7. SEPARABLE AND INSEPARABLE DEGREES; PROBLEMS; 3.8. NORMS AND TRACES; 3.8.1. Examples; PROBLEMS; 3.9. CYCLIC EXTENSIONS; PROBLEMS; 3.10. SOLVABILITY BY RADICALS; PROBLEMS; 3.11. FINITE FIELDS; 3.11.4. Examples; PROBLEMS; 3.12. INFINITE GALOIS THEORY; PROBLEMS; NOTES; Suggestions for further reading; Chapter 4 Transcendental Extensions; 4.1. DIMENSIONAL OPERATORS; 4.1.1. Examples; 4.1.2. Examples; PROBLEMS; 4.2. TRANSCENDENCE BASES AND TRANSCENDENCE DEGREE; PROBLEMS 4.3. SPECIALIZATIONS AND PLACES OF FIELDS4.3.1. Examples; PROBLEMS; 4.4. SEPARABLE EXTENSIONS; PROBLEMS; 4.5. DERIVATIONS OF FIELDS; 4.5.1. Examples; 4.5.5. Examples; PROBLEMS; 4.6. DERIVATIONS OF ALGEBRAIC FUNCTION FIELDS; PROBLEMS; NOTES; Suggestions for further reading; References and Selected Bibliography; Bibliography; Of historical interest; Index Field extensions (Mathematics) http://id.loc.gov/authorities/subjects/sh85048103 Galois theory. http://id.loc.gov/authorities/subjects/sh85052872 Extensions de corps (Mathématiques) Théorie de Galois. MATHEMATICS Algebra Intermediate. bisacsh Field extensions (Mathematics) fast Galois theory fast Galois-Theorie gnd http://d-nb.info/gnd/4155901-0 Körpererweiterung gnd http://d-nb.info/gnd/4164435-9 Galois, Théorie de. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048103 http://id.loc.gov/authorities/subjects/sh85052872 http://d-nb.info/gnd/4155901-0 http://d-nb.info/gnd/4164435-9 |
| 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 ; with a foreword by Roger Lyndon. |
| title_fullStr | Field extensions and Galois theory / Julio R. Bastida ; with a foreword by Roger Lyndon. |
| title_full_unstemmed | Field extensions and Galois theory / Julio R. Bastida ; with a foreword by Roger Lyndon. |
| title_short | Field extensions and Galois theory / |
| title_sort | field extensions and galois theory |
| topic | Field extensions (Mathematics) http://id.loc.gov/authorities/subjects/sh85048103 Galois theory. http://id.loc.gov/authorities/subjects/sh85052872 Extensions de corps (Mathématiques) Théorie de Galois. MATHEMATICS Algebra Intermediate. bisacsh Field extensions (Mathematics) fast Galois theory fast Galois-Theorie gnd http://d-nb.info/gnd/4155901-0 Körpererweiterung gnd http://d-nb.info/gnd/4164435-9 Galois, Théorie de. ram |
| topic_facet | Field extensions (Mathematics) Galois theory. Extensions de corps (Mathématiques) Théorie de Galois. MATHEMATICS Algebra Intermediate. Galois theory Galois-Theorie Körpererweiterung Galois, Théorie de. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=589162 |
| work_keys_str_mv | AT bastidajulior fieldextensionsandgaloistheory |