Introduction to field theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Pr.
1982
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 181 S. |
| ISBN: | 0521243882 0521286581 |
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| 100 | 1 | |a Adamson, Iain T. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to field theory |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Pr. |c 1982 | |
| 300 | |a VIII, 181 S. | ||
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Datensatz im Suchindex
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| adam_text | CONTENTS
PAGE
Prffacf. vii
CHAPTER I
ELEMENTARY DEFINITIONS
1. Rings and fields 1
2. Elementary properties 7
3. Homomorphisms 13
4. Vector spaces 19
5. Polynomials 26
6. Higher polynomial rings; rational functions 35
Examples I 38
CHAPTER II
EXTENSIONS OF FIELDS
7. Elementary properties 41
8. Simple extensions 46
9. Algebraic extensions 51
10. Factorisation of polynomials 53
11. Splitting fields 61
12. Algebraically closed fields 67
13. Separable extensions 69
Examples II 79
CHAPTER III
GALOIS THEORY
14. Automorphisms of fields 82
15. Normal extensions 89
16. The fundamental theorem of Galois theory 100
17. Norms and traces 0
18. The primitive element theorem; Lagrange s
theorem 1 3
19. Normal bases 118
Examples III 122
V
vi CONTENTS
CHAPTER IV
APPLICATIONS
PAGE
20. Finite fields 125
21. Cyclotomic extensions 130
22. Cyclotomic extensions of the rational number
field 134
23. Cyclic extensions 139
24. Wedderburn s theorem 145
25. Ruler and compasses constructions 149
26. Solution by radicals 160
27. Generic polynomials 168
Examples IV 173
Reading List 175
Index of Notations 176
Index 178
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:59:35Z |
| institution | BVB |
| isbn | 0521243882 0521286581 |
| language | English |
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| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Cambridge Univ. Pr. |
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| spelling | Adamson, Iain T. Verfasser aut Introduction to field theory 2. ed. Cambridge u.a. Cambridge Univ. Pr. 1982 VIII, 181 S. txt rdacontent n rdamedia nc rdacarrier Corps algébriques ram Algebraic fields Galois-Feld (DE-588)4155896-0 gnd rswk-swf Galois-Feld (DE-588)4155896-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002160763&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Adamson, Iain T. Introduction to field theory Corps algébriques ram Algebraic fields Galois-Feld (DE-588)4155896-0 gnd |
| subject_GND | (DE-588)4155896-0 |
| title | Introduction to field theory |
| title_auth | Introduction to field theory |
| title_exact_search | Introduction to field theory |
| title_full | Introduction to field theory |
| title_fullStr | Introduction to field theory |
| title_full_unstemmed | Introduction to field theory |
| title_short | Introduction to field theory |
| title_sort | introduction to field theory |
| topic | Corps algébriques ram Algebraic fields Galois-Feld (DE-588)4155896-0 gnd |
| topic_facet | Corps algébriques Algebraic fields Galois-Feld |
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