Quadratic forms over semilocal rings:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin, [u.a.]
Springer
1978
|
| Series: | Lecture notes in mathematics
655 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 199 Seiten |
| ISBN: | 3540088458 0387088458 |
Staff View
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| 100 | 1 | |a Baeza, Ricardo |d 1942- |0 (DE-588)139781633 |4 aut | |
| 245 | 1 | 0 | |a Quadratic forms over semilocal rings |c Ricardo Baeza |
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c 1978 | |
| 300 | |a VI, 199 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 655 | |
| 650 | 7 | |a Algèbre Clifford |2 Jussieu | |
| 650 | 7 | |a Anneau Witt |2 Jussieu | |
| 650 | 7 | |a Anneau semi-local |2 Jussieu | |
| 650 | 4 | |a Anneaux locaux | |
| 650 | 7 | |a Espace Pfister |2 Jussieu | |
| 650 | 4 | |a Formes (Mathématiques) | |
| 650 | 4 | |a Formes quadratiques | |
| 650 | 7 | |a Formes quadratiques |2 ram | |
| 650 | 7 | |a Forms, Quadratic |2 l | |
| 650 | 7 | |a Groupe orthogonal |2 Jussieu | |
| 650 | 4 | |a Mathématiques | |
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Record in the Search Index
| _version_ | 1810687498943201280 |
|---|---|
| adam_text |
Contents
Chapter I. Quadratic forms over rings 1
§1. Definitions 1
§2. Operations with quadratic and bilinear forms 5
§3. Subspaces 9
§4. Hyperbolic spaces 15
Chapter II. Invariants of quadratic forms 22
§1. Azumaya algebras 22
§2. Clifford algebras 30
§3. The structure of Clifford algebras 36
§4. Some computations 54
§5. Quadratic spaces of lower dimension 56
Chapter III. The orthogonal group 59
§1. Notations 59
§2. The Eichler decomposition of the orthogonal group 61
§3. Proper automorphisms 64
§4. Witt's cancellation theorem over semi local rings 79
§5. Transversality theorems for quadratic forms 83
Chapter IV. Pfister spaces over semi local rings 89
§1. Similarities 89
§2. Pfister spaces 94
§3. Isotropic Pfister spaces 105
§4. Further results on quadratic Pfister spaces 107
Chapter V. Structure of Witt rings 112
§1. Introduction 112
§2. The discriminant map 114
§3. Some computations 117
§4. Quadratic separable extensions 121
§5. An exact sequence of Witt groups 134
§6. The torsion of Wq(A) and W(A) 143
§7. The local global principle of Pfister 146
§8. Nilpotent elements in Wq(A) and W(A) 156
§9. An explicite description of Wq(A) 160
§10. On the classification of quadratic spaces 167
§11. The behaviour of Wq(A) by Galois extensions 173
VI
Appendix A. On the level of semi local rings 177
Appendix B. The u-invariant 187
References 193
Index 198 |
| any_adam_object | 1 |
| author | Baeza, Ricardo 1942- |
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| author_facet | Baeza, Ricardo 1942- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)605233929 (DE-599)BVBBV002252881 |
| dewey-full | 510.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.8 |
| dewey-search | 510.8 |
| dewey-sort | 3510.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-09-20T04:22:42Z |
| institution | BVB |
| isbn | 3540088458 0387088458 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001480384 |
| oclc_num | 605233929 |
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| physical | VI, 199 Seiten |
| psigel | TUB-nveb |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Baeza, Ricardo 1942- (DE-588)139781633 aut Quadratic forms over semilocal rings Ricardo Baeza Berlin, [u.a.] Springer 1978 VI, 199 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 655 Algèbre Clifford Jussieu Anneau Witt Jussieu Anneau semi-local Jussieu Anneaux locaux Espace Pfister Jussieu Formes (Mathématiques) Formes quadratiques Formes quadratiques ram Forms, Quadratic l Groupe orthogonal Jussieu Mathématiques Stellenring (DE-588)4183087-8 gnd rswk-swf Quadratische Form (DE-588)4128297-8 gnd rswk-swf Quadratische Form (DE-588)4128297-8 s Stellenring (DE-588)4183087-8 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-35816-9 Lecture notes in mathematics 655 (DE-604)BV000676446 655 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480384&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baeza, Ricardo 1942- Quadratic forms over semilocal rings Lecture notes in mathematics Algèbre Clifford Jussieu Anneau Witt Jussieu Anneau semi-local Jussieu Anneaux locaux Espace Pfister Jussieu Formes (Mathématiques) Formes quadratiques Formes quadratiques ram Forms, Quadratic l Groupe orthogonal Jussieu Mathématiques Stellenring (DE-588)4183087-8 gnd Quadratische Form (DE-588)4128297-8 gnd |
| subject_GND | (DE-588)4183087-8 (DE-588)4128297-8 |
| title | Quadratic forms over semilocal rings |
| title_auth | Quadratic forms over semilocal rings |
| title_exact_search | Quadratic forms over semilocal rings |
| title_full | Quadratic forms over semilocal rings Ricardo Baeza |
| title_fullStr | Quadratic forms over semilocal rings Ricardo Baeza |
| title_full_unstemmed | Quadratic forms over semilocal rings Ricardo Baeza |
| title_short | Quadratic forms over semilocal rings |
| title_sort | quadratic forms over semilocal rings |
| topic | Algèbre Clifford Jussieu Anneau Witt Jussieu Anneau semi-local Jussieu Anneaux locaux Espace Pfister Jussieu Formes (Mathématiques) Formes quadratiques Formes quadratiques ram Forms, Quadratic l Groupe orthogonal Jussieu Mathématiques Stellenring (DE-588)4183087-8 gnd Quadratische Form (DE-588)4128297-8 gnd |
| topic_facet | Algèbre Clifford Anneau Witt Anneau semi-local Anneaux locaux Espace Pfister Formes (Mathématiques) Formes quadratiques Forms, Quadratic Groupe orthogonal Mathématiques Stellenring Quadratische Form |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480384&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT baezaricardo quadraticformsoversemilocalrings |