Finite dimensional division algebras over fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1996
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 278 S. |
| ISBN: | 3540570292 |
Internformat
MARC
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| 245 | 1 | 0 | |a Finite dimensional division algebras over fields |c Nathan Jacobson |
| 246 | 1 | 3 | |a Finite-dimensional division algebras over fields |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1996 | |
| 300 | |a VIII, 278 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Algèbre à division |2 ram | |
| 650 | 7 | |a Corps algébriques |2 ram | |
| 650 | 4 | |a Algebraic fields | |
| 650 | 4 | |a Division algebras | |
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Datensatz im Suchindex
| _version_ | 1804125375522930688 |
|---|---|
| adam_text | Table of Contents
I. Skew Polynominals and Division Algebras 1
1.1. Skew polynomial Rings 1
1.2. Arithmetic in a PID 10
1.3. Applications to Skew polynomial Rings 14
1.4. Cyclic and Generalized Cyclic Algebras 19
1.5. Generalized Differential Extensions 21
1.6. Reduced Characteristic Polynomial, Trace and Norm 24
1.7. Norm Conditions 29
1.8. Derivations of Purely Inseparable Extensions of Exponent One 31
1.9. Some Tensor Product Constructions 33
1.10. Twisted Laurent Series 37
1.11. Differential Laurent Series 38
II. Brauer Factor Sets and Noether Factor Sets 41
2.1. Frobenius Algebras 42
2.2. Commutative Frobenius Subalgebras 43
2.3. Brauer Factor Sets 45
2.4. Condition for Split Algebra. The Tensor Product Theorem 51
2.5. The Brauer Group Bi(K/F) 53
2.6. Crossed Products 56
2.7. The Exponent of a Central Simple Algebra 60
2.8. Central Division Algebras of Prescribed Exponent and Degree 62
2.9. Central Division Algebras of Degree 4 66
2.10. Non cyclic Division Algebras of Degree Four 76
2.11. A Criterion for Cyclicity of a Division Algebra of Prime Degree ... 80
2.12. Central Division Algebras of Degree Five 84
2.13. Inflation and Restriction for Crossed Products 86
2.14. Isomorphism of Br(F) and H2(F) 91
III. Galois Descent and Generic Splitting Fields 95
3.1. Galois Descent for Vector Spaces 96
3.2. Forms of Fields 99
3.3. Forms and Non commutative Cohomology 102
3.4. Grassmannians 107
3.5. Brauer Severi Varieties HI
viii Table of Contents
3.6. Properties of Brauer Severi Varieties 114
3.7. Brauer Severi Varieties and Brauer Fields 118
3.8. Generic Splitting Fields 123
3.9. Properties of Brauer Fields 125
3.10. Central Simple Algebras Split by a Brauer Field 130
3.11. Norm Hypersurface of a Central Simple Algebra 138
3.12. Variety of Rank One Elements 140
3.13. The Brauer Functor. Corestriction of Algebras 149
IV. p Algebras 154
4.1. The Frobenius Map and Purely Inseparable Splitting Fields 155
4.2. Similarity to Tensor Products of Cyclic Algebras 158
4.3. Galois Extensions of Prime Power Degree 162
4.4. Conditions for Cyclicity 166
4.5. Similarity to Cyclic Algebras 171
4.6. Generic Abelian Crossed Products 173
4.7. Non cyclic p Algebras 182
V. Simple Algebras with Involution 185
5.1. Generalities. Simple Algebras with Involution 186
5.2. Existence of Involutions in Simple Algebras 193
5.3. Reduced Norms of Special Jordan Algebras 197
5.4. Differential Calculus of Rational Maps 204
5.5. Basic Properties of Reduced Norms 205
5.6. Low Dimensional Involutorial Division Algebras. Positive Results 209
5.7. Some Counterexamples 221
5.8. Decomposition of Simple Algebras with Involution of Degree 4... 232
5.9. Multiplicative Properties of Reduced Norms 235
5.10. Isotopy and Norm Similarity 240
5.11. Special Universal Envelopes 247
5.12. Applications to Norm Similarities 256
5.13. The Jordan Algebra H(A, J) 262
References 275
|
| any_adam_object | 1 |
| author | Jacobson, Nathan 1910-1999 |
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| callnumber-raw | QA247.45 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| classification_tum | MAT 120f |
| ctrlnum | (OCoLC)35095954 (DE-599)BVBBV010885635 |
| dewey-full | 512/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.24 |
| dewey-search | 512/.24 |
| dewey-sort | 3512 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010885635 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:00:34Z |
| institution | BVB |
| isbn | 3540570292 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007279163 |
| oclc_num | 35095954 |
| open_access_boolean | |
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| physical | VIII, 278 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| spelling | Jacobson, Nathan 1910-1999 Verfasser (DE-588)119081873 aut Finite dimensional division algebras over fields Nathan Jacobson Finite-dimensional division algebras over fields Berlin [u.a.] Springer 1996 VIII, 278 S. txt rdacontent n rdamedia nc rdacarrier Algèbre à division ram Corps algébriques ram Algebraic fields Division algebras Divisionsalgebra (DE-588)4138776-4 gnd rswk-swf Körper Algebra (DE-588)4308063-7 gnd rswk-swf Divisionsalgebra (DE-588)4138776-4 s DE-604 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=007279163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jacobson, Nathan 1910-1999 Finite dimensional division algebras over fields Algèbre à division ram Corps algébriques ram Algebraic fields Division algebras Divisionsalgebra (DE-588)4138776-4 gnd Körper Algebra (DE-588)4308063-7 gnd |
| subject_GND | (DE-588)4138776-4 (DE-588)4308063-7 |
| title | Finite dimensional division algebras over fields |
| title_alt | Finite-dimensional division algebras over fields |
| title_auth | Finite dimensional division algebras over fields |
| title_exact_search | Finite dimensional division algebras over fields |
| title_full | Finite dimensional division algebras over fields Nathan Jacobson |
| title_fullStr | Finite dimensional division algebras over fields Nathan Jacobson |
| title_full_unstemmed | Finite dimensional division algebras over fields Nathan Jacobson |
| title_short | Finite dimensional division algebras over fields |
| title_sort | finite dimensional division algebras over fields |
| topic | Algèbre à division ram Corps algébriques ram Algebraic fields Division algebras Divisionsalgebra (DE-588)4138776-4 gnd Körper Algebra (DE-588)4308063-7 gnd |
| topic_facet | Algèbre à division Corps algébriques Algebraic fields Division algebras Divisionsalgebra Körper Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007279163&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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