A field guide to algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2005
|
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 195 S. Ill., graph. Darst. |
| ISBN: | 0387214283 |
Staff View
MARC
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| 100 | 1 | |a Chambert-Loir, Antoine |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A field guide to algebra |c Antoine Chambert-Loir |
| 264 | 1 | |a New York, NY |b Springer |c 2005 | |
| 300 | |a X, 195 S. |b Ill., graph. Darst. | ||
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| 490 | 0 | |a Undergraduate texts in mathematics | |
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Record in the Search Index
| _version_ | 1804132855089987584 |
|---|---|
| adam_text | Contents
1
Field extensions
........................................... 1
1.1
Constructions with ruler and compass
...................... 1
1.2
Fields
.................................................. 3
1.3
Field extensions
......................................... 9
1.4
Some classical impossibilities
.............................. 15
1.5
Symmetric functions
..................................... 19
1.6
Appendix: Transcendence of
e
and
π
....................... 22
Exercises
................................................... 26
2
Roots
...................................................... 31
2.1
Ring of remainders
...................................... 31
2.2
Splitting extensions
...................................... 34
2.3
Algebraically closed fields: algebraic closure
................. 35
2.4
Appendix: Structure of polynomial rings
.................... 40
2.5
Appendix: Quotient rings
................................. 43
2.6
Appendix: Puiseux s theorem
............................. 45
Exercises
................................................... 50
3
Galois theory
.............................................. 55
3.1
Homomorphisms of an extension in an algebraic closure
...... 55
3.2
Automorphism group of an extension
...................... 59
3.3
The Galois group as a permutation group
................... 64
3.4
Discriminant: resolvent polynomials
........................ 68
3.5
Finite fields
............................................. 73
Exercises
................................................... 75
4
A bit of group theory
...................................... 83
4.1
Groups (quick review of basic definitions)
................... 83
VIII Contents
4.2
Subgroups
.
,
.....,...,,,..,..,...,..,,.,,..,..,..,,..... 84
4.3
Group actions
..,,........,......,..,,................... 86
4.4
Normal subgroups; quotient groups
........................ 8?
4.5
Solvable groups;
nilpotent
groups
.......................... 90
4.6
Symmetric and alternating groups
......................... 92
4.7
Matrix groups
........................................... 96
Exercises
................................................... 100
б
Applications
............................................... 107
5.1
Constructibility with ruler and compass
.................... 107
5.2
Cyclotomy
....................___......................108
5.3
Composite extensions
,................................... 113
5.4
Cyclic extensions
........................................116
5.5
Equations with degrees up to
4............................ 118
5.6
Solving equations by radicals
.............................. 125
5.7
How (not) to compute Galois groups
....................... 129
5.8
Specializing Galois groups
................................132
5.9
Hilbert s irreducibility theorem
............................139
Exercises
..........,............,................,.......... 145
β
Algebraic theory of differential equations
..................151
6.1
Differential fields
........................................ 151
6.2
Differential extensions; construction of derivations
........... 154
6.3
Differential equations
....................................158
6.4
Picard-
Vessiot extensions
................................. 160
6.5
The differential Galois group; examples
..................... 184
6.6
The differential Galois correspondence
...................■. 169
6.7
Integration in finite terms, elementary extensions
............170
6.8
Appendix: Hilbert s
Nullstellensatz........................ 177
Exercises
..........................,........................ 179
Examination problems
.,....,,......,...,......................181
References
.......................................,............. 189
Index
.....................................,....................191
|
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| author | Chambert-Loir, Antoine |
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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 | Book |
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| id | DE-604.BV019401161 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:59:27Z |
| institution | BVB |
| isbn | 0387214283 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012863459 |
| oclc_num | 54953152 |
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| physical | X, 195 S. Ill., graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Chambert-Loir, Antoine Verfasser aut A field guide to algebra Antoine Chambert-Loir New York, NY Springer 2005 X, 195 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Algebra gtt Corps algébriques Lichamen (wiskunde) gtt Teoria de galois larpcal Álgebra larpcal Algebraic fields Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012863459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chambert-Loir, Antoine A field guide to algebra Algebra gtt Corps algébriques Lichamen (wiskunde) gtt Teoria de galois larpcal Álgebra larpcal Algebraic fields Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 |
| title | A field guide to algebra |
| title_auth | A field guide to algebra |
| title_exact_search | A field guide to algebra |
| title_full | A field guide to algebra Antoine Chambert-Loir |
| title_fullStr | A field guide to algebra Antoine Chambert-Loir |
| title_full_unstemmed | A field guide to algebra Antoine Chambert-Loir |
| title_short | A field guide to algebra |
| title_sort | a field guide to algebra |
| topic | Algebra gtt Corps algébriques Lichamen (wiskunde) gtt Teoria de galois larpcal Álgebra larpcal Algebraic fields Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra Corps algébriques Lichamen (wiskunde) Teoria de galois Álgebra Algebraic fields |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012863459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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