Galois theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1998
|
| Edition: | 3., corr. printing |
| Series: | Graduate texts in mathematics
101 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 152 S. |
| ISBN: | 354090980X |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804127230959288320 |
|---|---|
| adam_text | Contents
Acknowledgments
xiii
§1.
Galois
§2.
Influence of
Lagrange §3.
Quadratic equations
§4.
1700 b.c.
to
a.D. 1500 §5.
Solution of cubic
§6.
Solution of quartic
§7.
Impossibility of quintic
§8.
Newton
§9.
Symmetric polynomials in roots
§10.
Fundamental theorem on symmetric polynomials
§11.
Proof
§12.
Newton s theorem
§13.
Discriminants
First Exercise Set
13
§14.
Solution of cubic
§15. Lagrange
and Vandermonde
§16. Lagrange
resolvents
§17.
Solution of quartic again
§18.
Attempt at quintic
§19.
Lagrange s
Réflexions
Second Exercise Set
22
§20.
Cyclotomic equations
§21.
The cases
η
= 3, 5 §22.
η =
7, 11 §23.
General case
§24.
Two lemmas
§25.
Gauss s method
§26.
/»-gons
by
ruler and compass
§27.
Summary
Third Exercise Set
31
§28.
Resolvents
§29.
Lagrange s theorem
§30.
Proof
§31.
Galois resol¬
vents
§32.
Existence of Galois resolvents
§33.
Representation of the
splitting field as K(t)
§34.
Simple algebraic extensions
§35.
Euclidean
algorithm
§36.
Construction of simple algebraic extensions
§37.
Galois
method
Fourth Exercise Set
45
x¡¿
Contents
§38.
Review
§39.
Finite permutation groups
§40.
Subgroups, normal
subgroups
§41.
The Galois group of an equation
§42.
Examples
Fifth Exercise Set
56
§43.
Solvability by radicals
§44.
Reduction of the Galois group by a cyclic
extension
§45.
Solvable groups
§46.
Reduction to a normal subgroup of
index
ρ
§47.
Theorem on solution by radicals (assuming roots of unity)
§48.
Summary
Sixth Exercise Set
65
§49.
Splitting fields
§50.
Fundamental theorem of algebra (so-called)
§51.
Construction of a splitting field
§52.
Need for a factorization method
§53.
Three theorems on factorization methods
§54.
Uniqueness of factorization
of polynomials
§55.
Factorization over
Ζ
§56.
Over
Q
§57.
Gauss s
lemma, factorization over
Q
§58.
Over transcendental extensions
§59.
Of polynomials in two variables
§60.
Over algebraic extensions
§61.
Final
remarks
Seventh Exercise Set
81
§62.
Review of Galois theory
§63.
Fundamental theorem of Galois theory
(so-called)
§64.
Galois group of x
- 1 = 0
over
Q
§65.
Solvability of
the cyclotomic equation
§66.
Theorem on solution by radicals
§67.
Equations with literal coefficients
§68.
Equations of prime degree
§69.
Galois group of x
- 1 = 0
over
Q
§70.
Proof of the main proposition
§71.
Deduction of Lemma
2
of
§24
Eighth Exercise Set
97
Appendix
1.
Memoir on the Conditions for Solvability of Equations
by Radicals, by Evariste Galois
101
Appendix
2.
Synopsis
114
Appendix
3.
Groups
1
1
8
Answers to Exercises
123
List of Exercises
145
References
149
Index
151
|
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| id | DE-604.BV012580953 |
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| isbn | 354090980X |
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| physical | XII, 152 S. |
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| publisher | Springer |
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| spelling | Edwards, Harold M. 1936-2020 Verfasser (DE-588)117709700 aut Galois theory Harold M. Edwards 3., corr. printing Berlin [u.a.] Springer 1998 XII, 152 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 101 Teoria de galois larpcal Galois theory Körpertheorie (DE-588)4164455-4 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf 1\p (DE-588)4006432-3 Bibliografie gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Galois-Theorie (DE-588)4155901-0 s Algebraische Zahlentheorie (DE-588)4001170-7 s Körpertheorie (DE-588)4164455-4 s 3\p DE-604 Graduate texts in mathematics 101 (DE-604)BV000000067 101 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008544223&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Edwards, Harold M. 1936-2020 Galois theory Graduate texts in mathematics Teoria de galois larpcal Galois theory Körpertheorie (DE-588)4164455-4 gnd Galois-Theorie (DE-588)4155901-0 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4164455-4 (DE-588)4155901-0 (DE-588)4001170-7 (DE-588)4006432-3 (DE-588)4123623-3 |
| title | Galois theory |
| title_auth | Galois theory |
| title_exact_search | Galois theory |
| title_full | Galois theory Harold M. Edwards |
| title_fullStr | Galois theory Harold M. Edwards |
| title_full_unstemmed | Galois theory Harold M. Edwards |
| title_short | Galois theory |
| title_sort | galois theory |
| topic | Teoria de galois larpcal Galois theory Körpertheorie (DE-588)4164455-4 gnd Galois-Theorie (DE-588)4155901-0 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | Teoria de galois Galois theory Körpertheorie Galois-Theorie Algebraische Zahlentheorie Bibliografie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008544223&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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