Algebra with Galois theory:
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| Previous Title: | Artin, Emil Modern higher algebra |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Courant Inst. of Math. Sciences [u.a.]
2007
|
| Series: | Courant lecture notes in mathematics
15 |
| Subjects: | |
| Online Access: | Table of contents Inhaltsverzeichnis |
| Physical Description: | VII, 126 S. graph. Darst. |
| ISBN: | 9780821841297 0821841297 |
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MARC
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| 100 | 1 | |a Artin, Emil |d 1898-1962 |e Verfasser |0 (DE-588)119045125 |4 aut | |
| 245 | 1 | 0 | |a Algebra with Galois theory |c Emil Artin. Notes by Albert A. Blank |
| 264 | 1 | |a New York, NY |b Courant Inst. of Math. Sciences [u.a.] |c 2007 | |
| 300 | |a VII, 126 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Courant lecture notes in mathematics |v 15 | |
| 650 | 4 | |a Galois theory | |
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| 780 | 0 | 0 | |i Frühere Auflage |a Artin, Emil |t Modern higher algebra |
| 830 | 0 | |a Courant lecture notes in mathematics |v 15 |w (DE-604)BV012714106 |9 15 | |
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Record in the Search Index
| _version_ | 1804137664397443072 |
|---|---|
| adam_text | Contents
Editors Note
vii
Chapter
1.
Groups
1
1.1.
The Concept of a Group
3
1.2.
Subgroups
4
Chapter
2.
Rings and Fields
11
2.1.
Linear Equations in a Field
13
2.2.
Vector Spaces
15
Chapter
3.
Polynomials. Factorization into Primes. Ideals.
21
3.1.
Polynomials over a Field
21
3.2.
Factorization into Primes
25
3.3.
Ideals
26
3.4.
Greatest Common Divisor
27
Chapter
4.
Solution of the General Equation of «th Degree. Residue Classes.
Extension Fields. Isomorphisms.
33
4.1.
Congruence
33
4.2.
Extension Fields
37
4.3.
Isomorphism
41
Chapter
5.
Galois Theory
49
5.1.
Splitting Fields
49
5.2.
Automorphisms of the Splitting Field
51
5.3.
The Characteristic of a Field
53
5.4.
Derivative of a Polynomial: Multiple Roots
55
5.5.
The Degree of an Extension Field
58
5.6.
Group Characters
60
5.7.
Automorphic Groups of a Field
63
5.8.
Fundamental Theorem of Galois Theory
69
5.9.
Finite Fields
75
Chapter
6.
Polynomials with Integral Coefficients
81
6.1.
Irreducibility
84
6.2.
Primitive Roots of Unity
87
Chapter
7.
The Theory of Equations
9
1
7.1.
Ruler and Compass Constructions
91
CONTENTS
7.2.
Solution
of Equations by Radicals
94
7.3.
Steinitz Theorem
104
7.4.
Towers of Fields
107
7.5.
Permutation Groups
112
7.6.
Abel s Theorem
121
7.7.
Polynomials of Prime Degree
123
|
| adam_txt |
Contents
Editors' Note
vii
Chapter
1.
Groups
1
1.1.
The Concept of a Group
3
1.2.
Subgroups
4
Chapter
2.
Rings and Fields
11
2.1.
Linear Equations in a Field
13
2.2.
Vector Spaces
15
Chapter
3.
Polynomials. Factorization into Primes. Ideals.
21
3.1.
Polynomials over a Field
21
3.2.
Factorization into Primes
25
3.3.
Ideals
26
3.4.
Greatest Common Divisor
27
Chapter
4.
Solution of the General Equation of «th Degree. Residue Classes.
Extension Fields. Isomorphisms.
33
4.1.
Congruence
33
4.2.
Extension Fields
37
4.3.
Isomorphism
41
Chapter
5.
Galois Theory
49
5.1.
Splitting Fields
49
5.2.
Automorphisms of the Splitting Field
51
5.3.
The Characteristic of a Field
53
5.4.
Derivative of a Polynomial: Multiple Roots
55
5.5.
The Degree of an Extension Field
58
5.6.
Group Characters
60
5.7.
Automorphic Groups of a Field
63
5.8.
Fundamental Theorem of Galois Theory
69
5.9.
Finite Fields
75
Chapter
6.
Polynomials with Integral Coefficients
81
6.1.
Irreducibility
84
6.2.
Primitive Roots of Unity
87
Chapter
7.
The Theory of Equations
9
1
7.1.
Ruler and Compass Constructions
91
CONTENTS
7.2.
Solution
of Equations by Radicals
94
7.3.
Steinitz' Theorem
104
7.4.
Towers of Fields
107
7.5.
Permutation Groups
112
7.6.
Abel's Theorem
121
7.7.
Polynomials of Prime Degree
123 |
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| author | Artin, Emil 1898-1962 |
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| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)159822590 (DE-599)BVBBV023324191 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T20:54:53Z |
| indexdate | 2024-07-09T21:15:53Z |
| institution | BVB |
| isbn | 9780821841297 0821841297 |
| language | English |
| lccn | 2007060799 |
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| physical | VII, 126 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Courant Inst. of Math. Sciences [u.a.] |
| record_format | marc |
| series | Courant lecture notes in mathematics |
| series2 | Courant lecture notes in mathematics |
| spelling | Artin, Emil 1898-1962 Verfasser (DE-588)119045125 aut Algebra with Galois theory Emil Artin. Notes by Albert A. Blank New York, NY Courant Inst. of Math. Sciences [u.a.] 2007 VII, 126 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Courant lecture notes in mathematics 15 Galois theory Algebra Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s DE-604 Blank, Albert A. Sonstige oth Erscheint auch als Online-Ausgabe 978-1-4704-3115-0 Frühere Auflage Artin, Emil Modern higher algebra Courant lecture notes in mathematics 15 (DE-604)BV012714106 15 http://www.loc.gov/catdir/toc/fy0803/2007060799.html Table of contents Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016508235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Artin, Emil 1898-1962 Algebra with Galois theory Courant lecture notes in mathematics Galois theory Algebra Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 |
| title | Algebra with Galois theory |
| title_auth | Algebra with Galois theory |
| title_exact_search | Algebra with Galois theory |
| title_exact_search_txtP | Algebra with Galois theory |
| title_full | Algebra with Galois theory Emil Artin. Notes by Albert A. Blank |
| title_fullStr | Algebra with Galois theory Emil Artin. Notes by Albert A. Blank |
| title_full_unstemmed | Algebra with Galois theory Emil Artin. Notes by Albert A. Blank |
| title_old | Artin, Emil Modern higher algebra |
| title_short | Algebra with Galois theory |
| title_sort | algebra with galois theory |
| topic | Galois theory Algebra Algebra (DE-588)4001156-2 gnd |
| topic_facet | Galois theory Algebra |
| url | http://www.loc.gov/catdir/toc/fy0803/2007060799.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016508235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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