Galois theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2006
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XI, 185 S. |
| ISBN: | 0387287256 9780387287256 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface
1
1.1
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
viii Contents
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
5
5.1
5.2
5.3
5.4
5.5
A Some Results from Group Theory
A.1 Solvable Groups
A.2 p-Groups
A.3 Symmetric and Alternating Groups
B A Lemma on Constructing Fields
C A Lemma from Elementary Number Theory
Index
Classical Galois theory is a subject generally acknowledged to be one of the most central and
beautiful areas in pure mathematics. This text develops the subject systematically and from the
beginning, requiring of the reader only basic facts about polynomials and a good knowledge of
linear algebra.
Key topics and features of this book:
•
•
able, and Galois extensions, and the Fundamental Theorem of Galois Theory;
•
cydotomic fields, algebraic number fields, solvability of equations by radicals, and the impossi¬
bility of solution of the three geometric problems of Greek antiquity;
•
The book discusses Galois theory in considerable generality, treating fields of characteristic zero and
of positive characteristic with consideration of both separable and inseparable extensions, but with
a particular emphasis on algebraic extensions of the field of rational numbers. While most of the
book is concerned with finite extensions, it concludes with a discussion of algebraic closure and of
infinite Galois extensions,
|
| adam_txt |
Contents
Preface
1
1.1
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
viii Contents
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
5
5.1
5.2
5.3
5.4
5.5
A Some Results from Group Theory
A.1 Solvable Groups
A.2 p-Groups
A.3 Symmetric and Alternating Groups
B A Lemma on Constructing Fields
C A Lemma from Elementary Number Theory
Index
Classical Galois theory is a subject generally acknowledged to be one of the most central and
beautiful areas in pure mathematics. This text develops the subject systematically and from the
beginning, requiring of the reader only basic facts about polynomials and a good knowledge of
linear algebra.
Key topics and features of this book:
•
•
able, and Galois extensions, and the Fundamental Theorem of Galois Theory;
•
cydotomic fields, algebraic number fields, solvability of equations by radicals, and the impossi¬
bility of solution of the three geometric problems of Greek antiquity;
•
The book discusses Galois theory in considerable generality, treating fields of characteristic zero and
of positive characteristic with consideration of both separable and inseparable extensions, but with
a particular emphasis on algebraic extensions of the field of rational numbers. While most of the
book is concerned with finite extensions, it concludes with a discussion of algebraic closure and of
infinite Galois extensions, |
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| ctrlnum | (OCoLC)255418248 (DE-599)BVBBV021244211 |
| dewey-full | 512.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| isbn | 0387287256 9780387287256 |
| language | English |
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| physical | XI, 185 S. |
| publishDate | 2006 |
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| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Weintraub, Steven H. 1951- Verfasser (DE-588)113001770 aut Galois theory Steven H. Weintraub New York, NY [u.a.] Springer 2006 XI, 185 S. txt rdacontent n rdamedia nc rdacarrier Universitext Galois-Theorie Galois-Theorie (DE-588)4155901-0 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Galois-Theorie (DE-588)4155901-0 s DE-604 Digitalisierung UBPassau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014565724&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014565724&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Weintraub, Steven H. 1951- Galois theory Galois-Theorie Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4155901-0 (DE-588)4123623-3 |
| title | Galois theory |
| title_auth | Galois theory |
| title_exact_search | Galois theory |
| title_exact_search_txtP | Galois theory |
| title_full | Galois theory Steven H. Weintraub |
| title_fullStr | Galois theory Steven H. Weintraub |
| title_full_unstemmed | Galois theory Steven H. Weintraub |
| title_short | Galois theory |
| title_sort | galois theory |
| topic | Galois-Theorie Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Galois-Theorie Lehrbuch |
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