Fields and Galois Theory:
This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolub...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Springer
2006
|
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection. Topics covered include rings and fields, integral domains and polynomials, field extensions and splitting fields, applications to geometry, finite fields, the Galois group, equations. Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided. |
| Beschreibung: | X, 227 S. graph. Darst. |
| ISBN: | 1852339861 9781852339869 ebook 1846281814 |
Internformat
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| 300 | |a X, 227 S. |b graph. Darst. | ||
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| 490 | 0 | |a Springer undergraduate mathematics series | |
| 520 | 3 | |a This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection. Topics covered include rings and fields, integral domains and polynomials, field extensions and splitting fields, applications to geometry, finite fields, the Galois group, equations. Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided. | |
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| 650 | 4 | |a Galois, Théorie de | |
| 650 | 4 | |a Algebraic fields | |
| 650 | 4 | |a Galois theory | |
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Datensatz im Suchindex
| _version_ | 1804135242415472640 |
|---|---|
| adam_text | Contents
Preface
Contents
1. Rings
1.1
1.2
1.3
1.4
1.5
2.
2.1
2.2
2.3
2.4
3.
3.1
3.2
3.3
4.
4.1
4.2
5.
x Contents
6.
7.
7.1
7.2
7.3
7.4
7.5
7.6
7.7
8.
8.1
8.2
8.3
9.
9.1
9.2
9.3
9.4
10.
10.1
10.2
10.3
11.
11.1
11.2
12.
Bibliography
List of Symbols
Index
|
| adam_txt |
Contents
Preface
Contents
1. Rings
1.1
1.2
1.3
1.4
1.5
2.
2.1
2.2
2.3
2.4
3.
3.1
3.2
3.3
4.
4.1
4.2
5.
x Contents
6.
7.
7.1
7.2
7.3
7.4
7.5
7.6
7.7
8.
8.1
8.2
8.3
9.
9.1
9.2
9.3
9.4
10.
10.1
10.2
10.3
11.
11.1
11.2
12.
Bibliography
List of Symbols
Index |
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| author | Howie, John M. 1936- |
| author_GND | (DE-588)122603427 |
| author_facet | Howie, John M. 1936- |
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| author_sort | Howie, John M. 1936- |
| author_variant | j m h jm jmh |
| building | Verbundindex |
| bvnumber | BV021508022 |
| callnumber-first | Q - Science |
| callnumber-label | QA214 |
| callnumber-raw | QA214 |
| callnumber-search | QA214 |
| callnumber-sort | QA 3214 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| classification_tum | MAT 126f |
| ctrlnum | (OCoLC)61441352 (DE-599)BVBBV021508022 |
| dewey-full | 512.74 512/.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.74 512/.32 |
| dewey-search | 512.74 512/.32 |
| dewey-sort | 3512.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| index_date | 2024-07-02T14:17:50Z |
| indexdate | 2024-07-09T20:37:23Z |
| institution | BVB |
| isbn | 1852339861 9781852339869 ebook 1846281814 |
| language | English |
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| spelling | Howie, John M. 1936- Verfasser (DE-588)122603427 aut Fields and Galois Theory John M. Howie London [u.a.] Springer 2006 X, 227 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection. Topics covered include rings and fields, integral domains and polynomials, field extensions and splitting fields, applications to geometry, finite fields, the Galois group, equations. Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided. Corps algébriques Galois, Théorie de Algebraic fields Galois theory Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Algebraischer Körper (DE-588)4141852-9 gnd rswk-swf Algebraischer Körper (DE-588)4141852-9 s Galois-Theorie (DE-588)4155901-0 s DE-604 Digitalisierung UBRegensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014724670&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Howie, John M. 1936- Fields and Galois Theory Corps algébriques Galois, Théorie de Algebraic fields Galois theory Galois-Theorie (DE-588)4155901-0 gnd Algebraischer Körper (DE-588)4141852-9 gnd |
| subject_GND | (DE-588)4155901-0 (DE-588)4141852-9 |
| title | Fields and Galois Theory |
| title_auth | Fields and Galois Theory |
| title_exact_search | Fields and Galois Theory |
| title_exact_search_txtP | Fields and Galois Theory |
| title_full | Fields and Galois Theory John M. Howie |
| title_fullStr | Fields and Galois Theory John M. Howie |
| title_full_unstemmed | Fields and Galois Theory John M. Howie |
| title_short | Fields and Galois Theory |
| title_sort | fields and galois theory |
| topic | Corps algébriques Galois, Théorie de Algebraic fields Galois theory Galois-Theorie (DE-588)4155901-0 gnd Algebraischer Körper (DE-588)4141852-9 gnd |
| topic_facet | Corps algébriques Galois, Théorie de Algebraic fields Galois theory Galois-Theorie Algebraischer Körper |
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