Fields and rings:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chicago
<<The>> Univ. of Chicago Press
1972
|
| Edition: | 2. ed. |
| Series: | Chicago lectures in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 206 S. |
| ISBN: | 0226424502 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804117251525181440 |
|---|---|
| adam_text | CONTENTS
PREFACE ix
Part I. FIELDS
Introduction 1
1. Field extensions 2
2. Ruler and compass constructions 8
3. Foundations of Galois theory 10
4. Normality and stability 19
5. Splitting fields 23
6. Radical extensions 32
7. The trace and norm theorems 39
8. Finite fields 45
9. Simple extensions 48
10. Cubic and quartic equations 50
11. Separability 55
12. Miscellaneous results on radical
extensions 60
13. Infinite algebraic extensions 74
Part II. RINGS
Introduction 79
1. The radical 81
2. Primitive rings and the
density theorem 91
3. Semi simple rings 107
4. The Wedderburn principal theorem 124
5. Theorems of Hopkins and Levitzki 132
v
CONTENTS
6. Primitive rings with minimal ideals
and dual vector spaces 139
7. Simple rings 147
(1) The enveloping ring and
the centroid 147
(2) Tensor products 150
(3) Maximal subfields 154
(4) Polynomial identities 156
(5) Extension of isomorphisms 161
Part III. HOMOLOGICAL DIMENSION
Introduction 165
1. Dimension of modules 167
2. Global dimension 171
3. First theorem on change of rings 171
4. Polynomial rings 174
5. Second theorem on change of rings 176
6. Third theorem on change of rings 177
7. Localization 181
8. Preliminary lemmas 182
9. A regular ring has finite
global dimension 183
10. A local ring of finite global dimension
is regular 183
11. Injective modules 185
vi
CONTENTS
12. The group of homomorphisms 187
13. The vanishing of Ext 187
14. Injective dimension 190
NOTES 193
INDEX 201
vii
|
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| indexdate | 2024-07-09T15:51:26Z |
| institution | BVB |
| isbn | 0226424502 |
| language | English |
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| physical | X, 206 S. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
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| publisher | <<The>> Univ. of Chicago Press |
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| series2 | Chicago lectures in mathematics |
| spelling | Kaplansky, Irving 1917-2006 Verfasser (DE-588)119264358 aut Fields and rings Irving Kaplansky 2. ed. Chicago <<The>> Univ. of Chicago Press 1972 X, 206 S. txt rdacontent n rdamedia nc rdacarrier Chicago lectures in mathematics Algebra Comutativa larpcal Anneaux (Algèbre) Corps algébriques Galois, Théorie de Galois-theorie gtt Lichamen (wiskunde) gtt Ringen (wiskunde) gtt Algebraic fields Galois theory Rings (Algebra) Körpertheorie (DE-588)4164455-4 gnd rswk-swf Körper Algebra (DE-588)4308063-7 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 s DE-604 Körpertheorie (DE-588)4164455-4 s Körper Algebra (DE-588)4308063-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001853155&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaplansky, Irving 1917-2006 Fields and rings Algebra Comutativa larpcal Anneaux (Algèbre) Corps algébriques Galois, Théorie de Galois-theorie gtt Lichamen (wiskunde) gtt Ringen (wiskunde) gtt Algebraic fields Galois theory Rings (Algebra) Körpertheorie (DE-588)4164455-4 gnd Körper Algebra (DE-588)4308063-7 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| subject_GND | (DE-588)4164455-4 (DE-588)4308063-7 (DE-588)4128084-2 |
| title | Fields and rings |
| title_auth | Fields and rings |
| title_exact_search | Fields and rings |
| title_full | Fields and rings Irving Kaplansky |
| title_fullStr | Fields and rings Irving Kaplansky |
| title_full_unstemmed | Fields and rings Irving Kaplansky |
| title_short | Fields and rings |
| title_sort | fields and rings |
| topic | Algebra Comutativa larpcal Anneaux (Algèbre) Corps algébriques Galois, Théorie de Galois-theorie gtt Lichamen (wiskunde) gtt Ringen (wiskunde) gtt Algebraic fields Galois theory Rings (Algebra) Körpertheorie (DE-588)4164455-4 gnd Körper Algebra (DE-588)4308063-7 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| topic_facet | Algebra Comutativa Anneaux (Algèbre) Corps algébriques Galois, Théorie de Galois-theorie Lichamen (wiskunde) Ringen (wiskunde) Algebraic fields Galois theory Rings (Algebra) Körpertheorie Körper Algebra Ring Mathematik |
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