A survey of trace forms of algebraic number fields:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore
World Scientific
1984
|
| Series: | Series in pure mathematics
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 316 S. |
| ISBN: | 9971966042 9971966050 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV002183998 | ||
| 003 | DE-604 | ||
| 005 | 20090616 | ||
| 007 | t | ||
| 008 | 890928s1984 |||| 00||| eng d | ||
| 020 | |a 9971966042 |9 9-971966-04-2 | ||
| 020 | |a 9971966050 |9 9-971966-05-0 | ||
| 020 | |a 9971966042 |9 9971-966-04-2 | ||
| 020 | |a 9971966050 |9 9971-966-05-0 | ||
| 035 | |a (OCoLC)11695676 | ||
| 035 | |a (DE-599)BVBBV002183998 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-384 |a DE-355 |a DE-29T |a DE-19 |a DE-706 |a DE-83 |a DE-11 | ||
| 050 | 0 | |a QA247 | |
| 082 | 0 | |a 512.74 |2 19 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a MAT 126f |2 stub | ||
| 100 | 1 | |a Conner, Pierre E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A survey of trace forms of algebraic number fields |c P. E. Conner & R. Perlis |
| 264 | 1 | |a Singapore |b World Scientific |c 1984 | |
| 300 | |a IX, 316 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series in pure mathematics |v 2 | |
| 650 | 7 | |a Algebraïsche getallen |2 gtt | |
| 650 | 7 | |a Extensions de corps (mathématiques) |2 ram | |
| 650 | 7 | |a Formules de trace |2 ram | |
| 650 | 7 | |a Matematica |2 larpcal | |
| 650 | 4 | |a Field extensions (Mathematics) | |
| 650 | 4 | |a Ring extensions (Algebra) | |
| 650 | 4 | |a Trace formulas | |
| 650 | 0 | 7 | |a Algebraischer Zahlkörper |0 (DE-588)4068537-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spurformel |0 (DE-588)4182612-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraischer Zahlkörper |0 (DE-588)4068537-8 |D s |
| 689 | 0 | 1 | |a Spurformel |0 (DE-588)4182612-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Perlis, R. |e Verfasser |4 aut | |
| 830 | 0 | |a Series in pure mathematics |v 2 |w (DE-604)BV000016845 |9 2 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001434544&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |q TUB-nvmb | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001434544 | ||
Record in the Search Index
| _version_ | 1804116639702056960 |
|---|---|
| adam_text | CONTENTS
Preface 1
CHAPTER I: THE WITT CLASS OF A TRACE FORM
1.1 Introduction 5
1.2 Witt Rings 8
1.3 Discriminant of an Algebraic Extension 22
1.4 Quadratic Extensions 25
1.5 Base Lifting 30
1.6 Product Decomposition 35
1.7 Multiples of Algebraic Classes 38
1.8 Normal Extensions of Degree 2 (Mod 4) 40
1.9 Normal Extensions of Even Degree 43
1.10 Torsion Classes in W(Q) 51
1.11 Normal Classes are Abelian in W(Q) 57
CHAPTER II: THE HASSE WITT INVARIANT OF A TRACE FORM
II. 1 Introduction 67
II. 2 Extensions of Finite Fields 68
II. 3 Unramified Local Extensions 75
II 4 Computation of 3 79
11.5 The Local Knebusch Sequence 84
11.6 Totally Ramified Extensions 91
II. 7 Algebraic Classes in W(Q ) 99
11.8 Normal Local Extensions 102
11.9 The Cycle Associated to a Witt Class 112
11.10 Classes of Even Signature are Algebraic 118
CHAPTER III: EXAMPLES OF TRACE FORMS ON EXTENSIONS OF Q
III. 1 Introduction 126
III. 2 Quadratic Extensions 127
III.3 Extensions of Degree 3 131
Ill. A Pure Equations 138
III. 5 Scaled Trace Forms 141
111.6 Witt Classes of Signature 1 148
111.7 Extensions of Degree 4 152
III. 8 A Modulo 4 Reciprocity Formula 158
III.9 Further Questions 166
CHAPTER IV: THE INTEGRAL TRACE FORM ON.A CYCLIC
EXTENSION OF ODD PRIME DEGREE
IV. 1 Introduction 169
IV. 2 Modules Over a Group Ring 171
IV. 3 Symmetric Circulants 173
IV. 4 Induced Circulants 174
IV.5 Product Circulants 177
IV. 6 The Group C 178
IV. 7 Tamely Ramified Extensions 186
IV.8 Lagrangian Basis 192
IV.9 The Wildly Ramified Case 196
IV. 10 The Ring Z q~ 199
IV. 11 The Ring 0 q~ 201
IV. 12 Examples 205
IV. 13 Conductors 211
IV. 14 Triviality of the Obs(F/Q) 213
IV. 15 A Fake Cyclic Extension 216
CHAPTER V: NORMAL EXTENSIONS AND EQUIVARIANT WITT RINGS
V. 1 Introduction 218
V.2 The Equivariant Witt Ring 220
V.3 A Multiplicative Relation 226
V.4 Odd Degree Normal Extensions of Q 230
V. 5 An invariant from Topology 231
V.6 Local Normal Extensions .....238
k+1
V.7 Cyclic Extensions of Degree 2 245
V.8 The Local Boundary 249
V.9 The Global Case 257
V.10 Cyclic Witt Classes 260
V.ll The Group W(Z,G) 266
V. 12 Appendix 271
CHAPTER VI. EXAMPLES AND APPLICATIONS OF TRACE FORM
CONSIDERATIONS
VI. 1 Introduction 281
VI.2 Irreducible Trinomials 285
VI.3 Normal Extensions with Non Square Discriminant...294
VI. 4 Solvable Trinomials 304
VI.5 Quintic Extensions 309
REFERENCES 314
|
| any_adam_object | 1 |
| author | Conner, Pierre E. Perlis, R. |
| author_facet | Conner, Pierre E. Perlis, R. |
| author_role | aut aut |
| author_sort | Conner, Pierre E. |
| author_variant | p e c pe pec r p rp |
| building | Verbundindex |
| bvnumber | BV002183998 |
| callnumber-first | Q - Science |
| callnumber-label | QA247 |
| callnumber-raw | QA247 |
| callnumber-search | QA247 |
| callnumber-sort | QA 3247 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| classification_tum | MAT 126f |
| ctrlnum | (OCoLC)11695676 (DE-599)BVBBV002183998 |
| dewey-full | 512.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.74 |
| dewey-search | 512.74 |
| dewey-sort | 3512.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02028nam a2200541 cb4500</leader><controlfield tag="001">BV002183998</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090616 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890928s1984 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9971966042</subfield><subfield code="9">9-971966-04-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9971966050</subfield><subfield code="9">9-971966-05-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9971966042</subfield><subfield code="9">9971-966-04-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9971966050</subfield><subfield code="9">9971-966-05-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)11695676</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002183998</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA247</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.74</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 126f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Conner, Pierre E.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A survey of trace forms of algebraic number fields</subfield><subfield code="c">P. E. Conner & R. Perlis</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore</subfield><subfield code="b">World Scientific</subfield><subfield code="c">1984</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 316 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Series in pure mathematics</subfield><subfield code="v">2</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Algebraïsche getallen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Extensions de corps (mathématiques)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Formules de trace</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Matematica</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Field extensions (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ring extensions (Algebra)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Trace formulas</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraischer Zahlkörper</subfield><subfield code="0">(DE-588)4068537-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Spurformel</subfield><subfield code="0">(DE-588)4182612-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraischer Zahlkörper</subfield><subfield code="0">(DE-588)4068537-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Spurformel</subfield><subfield code="0">(DE-588)4182612-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Perlis, R.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Series in pure mathematics</subfield><subfield code="v">2</subfield><subfield code="w">(DE-604)BV000016845</subfield><subfield code="9">2</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001434544&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">TUB-nvmb</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001434544</subfield></datafield></record></collection> |
| id | DE-604.BV002183998 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:41:43Z |
| institution | BVB |
| isbn | 9971966042 9971966050 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001434544 |
| oclc_num | 11695676 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-11 |
| physical | IX, 316 S. |
| psigel | TUB-nvmb |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in pure mathematics |
| series2 | Series in pure mathematics |
| spelling | Conner, Pierre E. Verfasser aut A survey of trace forms of algebraic number fields P. E. Conner & R. Perlis Singapore World Scientific 1984 IX, 316 S. txt rdacontent n rdamedia nc rdacarrier Series in pure mathematics 2 Algebraïsche getallen gtt Extensions de corps (mathématiques) ram Formules de trace ram Matematica larpcal Field extensions (Mathematics) Ring extensions (Algebra) Trace formulas Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Spurformel (DE-588)4182612-7 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 s Spurformel (DE-588)4182612-7 s DE-604 Perlis, R. Verfasser aut Series in pure mathematics 2 (DE-604)BV000016845 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001434544&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conner, Pierre E. Perlis, R. A survey of trace forms of algebraic number fields Series in pure mathematics Algebraïsche getallen gtt Extensions de corps (mathématiques) ram Formules de trace ram Matematica larpcal Field extensions (Mathematics) Ring extensions (Algebra) Trace formulas Algebraischer Zahlkörper (DE-588)4068537-8 gnd Spurformel (DE-588)4182612-7 gnd |
| subject_GND | (DE-588)4068537-8 (DE-588)4182612-7 |
| title | A survey of trace forms of algebraic number fields |
| title_auth | A survey of trace forms of algebraic number fields |
| title_exact_search | A survey of trace forms of algebraic number fields |
| title_full | A survey of trace forms of algebraic number fields P. E. Conner & R. Perlis |
| title_fullStr | A survey of trace forms of algebraic number fields P. E. Conner & R. Perlis |
| title_full_unstemmed | A survey of trace forms of algebraic number fields P. E. Conner & R. Perlis |
| title_short | A survey of trace forms of algebraic number fields |
| title_sort | a survey of trace forms of algebraic number fields |
| topic | Algebraïsche getallen gtt Extensions de corps (mathématiques) ram Formules de trace ram Matematica larpcal Field extensions (Mathematics) Ring extensions (Algebra) Trace formulas Algebraischer Zahlkörper (DE-588)4068537-8 gnd Spurformel (DE-588)4182612-7 gnd |
| topic_facet | Algebraïsche getallen Extensions de corps (mathématiques) Formules de trace Matematica Field extensions (Mathematics) Ring extensions (Algebra) Trace formulas Algebraischer Zahlkörper Spurformel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001434544&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000016845 |
| work_keys_str_mv | AT connerpierree asurveyoftraceformsofalgebraicnumberfields AT perlisr asurveyoftraceformsofalgebraicnumberfields |