The theory of algebraic number fields:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kon
Springer
1998
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 335 - 343 |
| Physical Description: | XXXVI, 350 S. |
| ISBN: | 3540627790 |
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| 240 | 1 | 0 | |a Die Theorie der algebraischen Zahlkörper |
| 245 | 1 | 0 | |a The theory of algebraic number fields |c David Hilbert. Transl. from the German by Iain T. Adamson. With an introd. by Franz Lemmermeyer and Norbert Schappacher |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kon |b Springer |c 1998 | |
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| 500 | |a Literaturverz. S. 335 - 343 | ||
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Record in the Search Index
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| adam_text |
DAVID HUBERT THE THEORY OF ALGEBRAIC NUMBER FIELDS TRANSLATED FROM THE
GERMAN BY LAIN T. ADAMSON WITH AN INTRODUCTION BY FRANZ LEMMERMEYER AND
NORBERT SCHAPPACHER TABLE OF CONTENTS TRANSLATOR'S PREFACE V HILBERT'S
PREFACE VII INTRODUCTION TO THE ENGLISH EDITION BY FRANZ LEMMERMEYER AND
NORBERT SCHAPPACHER XXIII 1. THE REPORT XXIII 2. LATER CRITICISM XXV 3.
KUMMER'S THEORY XXVIII 4. A FEW NOTEWORTHY DETAILS XXXII PART I. THE
THEORY OF GENERAL NUMBER FIELDS 1. ALGEBRAIC NUMBERS AND NUMBER FIELDS 3
§1. NUMBER FIELDS AND THEIR CONJUGATES 3 §2. ALGEBRAIC INTEGERS 4 §3.
NORM, DIFFERENT AND DISCRIMINANT OF A NUMBER. BASIS OF A NUMBER FIELD 5
2. IDEALS OF NUMBER FIELDS 9 §4. MULTIPLICATION AND DIVISIBILITY OF
IDEALS. PRIME IDEALS 9 §5. UNIQUE FACTORISATION OF AN IDEAL INTO PRIME
IDEALS 11 §6. FORMS OF NUMBER FIELDS AND THEIR CONTENTS 14 3.
CONGRUENCES WITH RESPECT TO IDEALS 17 §7. THE NORM OF AN IDEAL AND ITS
PROPERTIES 17 §8. FERMAT'S THEOREM IN IDEAL THEORY. THE FUNCTION IP(A)
20 §9. PRIMITIVE ROOTS FOR A PRIME IDEAL 22 4. THE DISCRIMINANT OF A
FIELD AND ITS DIVISORS 25 §10. THEOREM ON THE DIVISORS OF THE
DISCRIMINANT. LEMMA ON INTEGRAL FUNCTIONS 25 §11. FACTORISATION AND
DISCRIMINANT OF THE FUNDAMENTAL EQUATION 28 XIV TABLE OF CONTENTS §12.
ELEMENTS AND DIFFERENT OF A FIELD. PROOF OF THE THEOREM ON THE DIVISORS
OF THE DISCRIMINANT OF A FIELD 30 §13. DETERMINATION OF PRIME IDEALS.
CONSTANT NUMERICAL FACTORS OF THE RATIONAL UNIT FORM U 31 5. EXTENSION
FIELDS 33 §14. RELATIVE NORMS, DIFFERENTS AND DISCRIMINANTS 33 §15.
PROPERTIES OF THE RELATIVE DIFFERENT AND DISCRIMINANT 35 §16.
DECOMPOSITION OF AN ELEMENT OF A FIELD K IN AN EXTENSION K. THEOREM ON
THE DIFFERENT OF THE EXTENSION K 38 6. UNITS OF A FIELD 41 §17.
EXISTENCE OF CONJUGATES WITH ABSOLUTE VALUES SATISFYING CERTAIN
INEQUALITIES 41 §18. ABSOLUTE VALUE OF THE FIELD DISCRIMINANT 43 §19.
THEOREM ON THE EXISTENCE OF UNITS 45 §20. PROOF OF THE THEOREM ON THE
EXISTENCE OF UNITS 49 §21. FUNDAMENTAL SETS OF UNITS. REGULATOR OF A
FIELD. INDEPENDENT SETS OF UNITS 51 7. IDEAL CLASSES OF A FIELD 53 §22.
IDEAL CLASSES. FINITENESS OF THE CLASS NUMBER 53 §23. APPLICATIONS OF
THE THEOREM ON THE FINITENESS OF THE CLASS NUMBER 54 §24. THE SET OF
IDEAL CLASSES. STRICT FORM OF THE CLASS CONCEPT . 56 §25. A LEMMA ON
THE ASYMPTOTIC VALUE OF THE NUMBER OF ALL PRINCIPAL IDEALS DIVISIBLE BY
A GIVEN IDEAL 56 §26. DETERMINATION OF THE CLASS NUMBER BY THE RESIDUE
OF THE FUNCTION ((S) AT S = 1 60 §27. ALTERNATIVE INFINITE EXPANSIONS OF
THE FUNCTION ((S) 62 §28. COMPOSITION OF IDEAL CLASSES OF A FIELD 62
§29. CHARACTERS OF IDEAL CLASSES. GENERALISATION OF THE FUNCTION ((S) 64
8. REDUCIBLE FORMS OF A FIELD 65 §30. REDUCIBLE FORMS. FORM CLASSES AND
THEIR COMPOSITION 65 9. ORDERS IN A FIELD 67 §31. ORDERS. ORDER IDEALS
AND THEIR MOST IMPORTANT PROPERTIES . 67 §32. ORDER DETERMINED BY AN
INTEGER. THEOREM ON THE DIFFERENT OF AN INTEGER OF A FIELD 69 §33.
REGULAER ORDER IDEALS AND THEIR DIVISIBILITY LAWS 72 §34. UNITS OF AN
ORDER. ORDER IDEAL CLASSES 73 §35. LATTICES AND LATTICE CLASSES 74 TABLE
OF CONTENTS XV PART II. GALOIS NUMBER FIELDS 10. PRIME IDEALS OF A
GALOIS NUMBER FIELD AND ITS SUBFIELDS . . 79 §36. UNIQUE FACTORISATION
OF THE IDEALS OF A GALOIS NUMBER FIELD INTO PRIME IDEALS 79 §37.
ELEMENTS, DIFFERENT AND DISCRIMINANT OF A GALOIS NUMBER FIELD 81 §38.
SUBFIELDS OF A GALOIS NUMBER FIELD 81 §39. DECOMPOSITION FIELD AND
INERTIA FIELD OF A PRIME IDEAL 82 §40. A THEOREM ON THE DECOMPOSITION
FIELD 83 §41. THE RAMIFICATION FIELD OF A PRIME IDEAL 84 §42. A THEOREM
ON THE INERTIA FIELD 85 §43. THEOREMS ON THE RAMIFICATION GROUP AND
RAMIFICATION FIELD . 86 §44. HIGHER RAMIFICATION GROUPS OF A PRIME IDEAL
86 §45. SUMMARY OF THE THEOREMS ON THE DECOMPOSITION OF A RATIONAL PRIME
NUMBER P IN A GALOIS NUMBER FIELD 87 11. THE DIFFERENTS AND
DISCRIMINANTS OF A GALOIS NUMBER FIELD AND ITS SUBFIELDS 89 §46. THE
DIFFERENTS OF THE INERTIA FIELD AND THE RAMIFICATION FIELD 89 §47. THE
DIVISORS OF THE DISCRIMINANT OF A GALOIS NUMBER FIELD . 90 12.
CONNEXION BETWEEN THE ARITHMETIC AND ALGEBRAIC PROPERTIES OF A GALOIS
NUMBER FIELD 93 §48. GALOIS, ABELIAN AND CYCLIC EXTENSION FIELDS 93 §49.
ALGEBRAIC PROPERTIES OF THE INERTIA FIELD AND THE RAMIFICATION FIELD.
REPRESENTATION OF THE NUMBERS OF A GALOIS NUMBER FIELD BY RADICALS OVER
THE DECOMPOSITION FIELD 94 §50. THE DENSITY OF PRIME IDEALS OF DEGREE 1
AND THE CONNEXION BETWEEN THIS DENSITY AND THE ALGEBRAIC PROPERTIES OF A
NUMBER FIELD 94 13. COMPOSITION OF NUMBER FIELDS 97 §51. THE GALOIS
NUMBER FIELD FORMED BY THE COMPOSITION OF A NUMBER FIELD AND ITS
CONJUGATES 97 §52. COMPOSITUM OF TWO FIELDS WHOSE DISCRIMINANTS ARE
RELATIVELY PRIME 98 14. THE PRIME IDEALS OF DEGREE 1 AND THE CLASS
CONCEPT 101 §53. GENERATION OF IDEAL CLASSES BY PRIME IDEALS OF DEGREE 1
101 15. CYCLIC EXTENSION FIELDS OF PRIME DEGREE 105 §54. SYMBOLIC
POWERS. THEOREM ON NUMBERS WITH RELATIVE NORM 1 105 XVI TABLE OF
CONTENTS §55. FUNDAMENTAL SETS OF RELATIVE UNITS AND PROOF OF THEIR
EXISTENCE 106 §56. EXISTENCE OF A UNIT IN K WITH RELATIVE NORM 1 WHICH
IS NOT THE QUOTIENT OF TWO RELATIVELY CONJUGATE UNITS 108 §57. AMBIG
IDEALS AND THE RELATIVE DIFFERENT OF A CYCLIC EXTENSION 109 §58.
FUNDAMENTAL THEOREM ON CYCLIC EXTENSIONS WITH RELATIVE DIFFERENT 1.
DESIGNATION OF THESE FIELDS AS CLASS FIELDS 111 PART III. QUADRATIC
NUMBER FIELDS 16. FACTORISATION OF NUMBERS IN QUADRATIC FIELDS 115 §59.
BASIS AND DISCRIMINANT OF A QUADRATIC FIELD 115 §60. PRIME IDEALS OF A
QUADRATIC FIELD 116 §61. THE SYMBOL (-) 118 \WJ §62. UNITS OF A
QUADRATIC FIELD 119 §63. COMPOSITION OF THE SET OF IDEAL CLASSES 119 17.
GENERA IN QUADRATIC FIELDS AND THEIR CHARACTER SETS 121 / FF FR) \ §64.
THE SYMBOL ( -I* 121 V W / §65. THE CHARACTER SET OF AN IDEAL 125 §66.
THE CHARACTER SET OF AN IDEAL CLASS AND THE CONCEPT OF GENUS 126 §67.
THE FUNDAMENTAL THEOREM ON THE GENERA OF QUADRATIC FIELDS 127 §68. A
LEMMA ON QUADRATIC FIELDS WHOSE DISCRIMINANTS ARE DIVISIBLE BY ONLY ONE
PRIME 127 §69. THE QUADRATIC RECIPROCITY LAW. A LEMMA ON THE SYMBOL (
^ ) 128 \ W / §70. PROOF OF THE RELATION ASSERTED IN THEOREM 100 BETWEEN
ALL THE CHARACTERS OF A GENUS 131 18. EXISTENCE OF GENERA IN QUADRATIC
FIELDS 133 §71. THEOREM ON THE NORMS OF NUMBERS IN A QUADRATIC FIELD 133
§72. THE CLASSES OF THE PRINCIPAL GENUS 135 §73. AMBIG IDEALS 136 §74.
AMBIG IDEAL CLASSES 136 §75. AMBIG CLASSES DETERMINED BY AMBIG IDEALS
136 §76. AMBIG IDEAL CLASSES CONTAINING NO AMBIG IDEALS 138 §77. THE
NUMBER OF ALL AMBIG IDEAL CLASSES 139 §78. ARITHMETIC PROOF OF THE
EXISTENCE OF GENERA 139 TABLE OF CONTENTS XVII §79. TRANSCENDENTAL
REPRESENTATION OF THE CLASS NUMBER AND AN APPLICATION THAT THE LIMIT OF
A CERTAIN INFINITE PRODUCT IS POSITIVE 140 §80. EXISTENCE OF INFINITELY
MANY RATIONAL PRIME NUMBERS MODULO WHICH GIVEN NUMBERS HAVE PRESCRIBED
QUADRATIC RESIDUE CHARACTERS 142 §81. EXISTENCE OF INFINITELY MANY PRIME
IDEALS WITH PRESCRIBED CHARACTERS IN A QUADRATIC FIELD 144 §82.
TRANSCENDENTAL PROOF OF THE EXISTENCE OF GENERA AND THE OTHER RESULTS
OBTAINED IN SECTIONS 71 TO 77 146 §83. STRICT FORM OF THE EQUIVALENCE
AND CLASS CONCEPTS 146 §84. THE FUNDAMENTAL THEOREM FOR THE NEW CLASS
AND GENUS CONCEPTS 147 19. DETERMINATION OF THE NUMBER OF IDEAL CLASSES
OF A QUADRATIC FIELD 149 §85. THE SYMBOL F * 1 FOR A COMPOSITE NUMBER N
149 §86. CLOSED FORM FOR THE NUMBER OF IDEAL CLASSES 150 §87. DIRICHLET
BIQUADRATIC NUMBER FIELDS 152 20. ORDERS AND MODULES OF QUADRATIC FIELDS
155 §88. ORDERS OF A QUADRATIC FIELD 155 §89. THEOREM ON THE MODULE
CLASSES OF A QUADRATIC FIELD. BINARY QUADRATIC FORMS 155 §90. LOWER AND
HIGHER THEORIES OF QUADRATIC FIELDS 157 PART IV. CYCLOTOMIC FIELDS 21.
THE ROOTS OF UNITY WITH PRIME NUMBER EXPONENT L AND THE CYCLOTOMIC FIELD
THEY GENERATE 161 §91. DEGREE OF THE CYCLOTOMIC FIELD OF THE L-TH ROOTS
OF UNITY; FACTORISATION OF THE PRIME NUMBER L 161 §92. BASIS AND
DISCRIMINANT OF THE CYCLOTOMIC FIELD OF THE L-TH ROOT S OF UNITY 162
§93. FACTORISATION OF THE RATIONAL PRIMES DISTINCT FROM L IN THE
CYCLOTOMIC FIELD OF THE L-TH ROOTS OF UNITY 163 22. THE ROOTS OF UNITY
FOR A COMPOSITE EXPONENT M AND THE CYCLOTOMIC FIELD THEY GENERATE 167
§94. THE CYCLOTOMIC FIELD OF THE M-TH ROOTS OF UNITY 167 §95. DEGREE OF
THE CYCLOTOMIC FIELD OF THE L H -TH ROOTS OF UNITY AND THE FACTORISATION
OF THE PRIME NUMBER L IN THIS FIELD . 168 XVIII TABLE OF CONTENTS §96.
BASIS AND DISCRIMINANT OF THE CYCLOTOMIC FIELD OF THE L H -TH ROOTS OF
UNITY 168 §97. THE CYCLOTOMIC FIELD OF THE M-TH ROOTS OF UNITY. DEGREE,
DISCRIMINANT AND PRIME IDEALS OF THIS FIELD 169 §98. UNITS OF THE
CYCLOTOMIC FIELD FC(E 2 */ M ). DEFINITION OF THE CYCLOTOMIC UNITS 171
23. CYCLOTOMIC FIELDS AS ABELIAN FIELDS 175 §99. THE GROUP OF THE
CYCLOTOMIC FIELD OF THE M-TH ROOTS OF UNITY 175 §100. THE GENERAL NOTION
OF CYCLOTOMIC FIELD. THE FUNDAMENTAL THEOREM ON ABELIAN FIELDS 176 §101.
A GENERAL LEMMA ON CYCLIC FIELDS 177 §102. CONCERNING CERTAIN PRIME
DIVISORS OF THE DISCRIMINANT OF A CYCLIC FIELD OF DEGREE L H 178 §103.
THE CYCLIC FIELD OF DEGREE U WHOSE DISCRIMINANT IS DIVISIBLE ONLY BY U
AND CYCLIC FIELDS OF DEGREE U H AND 2 H INCLUDING U\ AND II\
RESPECTIVELY AS SUBFIELDS 181 §104. PROOF OF THE FUNDAMENTAL THEOREM ON
ABELIAN FIELDS 184 24. THE ROOT NUMBERS OF THE CYCLOTOMIC FIELD OF THE
Z-TH ROOTS OF UNITY 187 §105. DEFINITION AND EXISTENCE OF NORMAL BASES
187 §106. ABELIAN FIELDS OF PRIME DEGREE L AND DISCRIMINANT P L ~ L .
ROOT NUMBERS OF THIS FIELD 188 §107. CHARACTERISTIC PROPERTIES OF ROOT
NUMBERS 188 §108. FACTORISATION OF THE Z-TH POWER OF A ROOT NUMBER IN
THE FIELD OF THE Z-TH ROOTS OF UNITY 192 §109. AN EQUIVALENCE FOR THE
PRIME IDEALS OF DEGREE 1 IN THE FIELD OF THE L-TH. ROOTS OF UNITY 193
§110. CONSTRUCTION OF ALL NORMAL BASES AND ROOT NUMBERS 194 §111. THE
LAGRANGE NORMAL BASIS AND THE LAGRANGE ROOT NUMBER 195 §112. THE
CHARACTERISTIC PROPERTIES OF THE LAGRANGE ROOT NUMBER 195 25. THE
RECIPROCITY LAW FOR L-TH. POWER RESIDUES BETWEEN A RATIONAL NUMBER AND A
NUMBER IN THE FIELD OF Z-TH ROOTS OF UNITY 199 §113. THE POWER CHARACTER
OF A NUMBER AND THE SYMBOL L * . 199 §114. A LEMMA ON THE POWER
CHARACTER OF THE Z-TH POWER OF THE LAGRANGE ROOT NUMBER 200 §115. PROOF
OF THE RECIPROCITY LAW IN THE FIELD K(() BETWEEN A RATIONAL NUMBER AND
AN ARBITRARY NUMBER 202 TABLE OF CONTENTS XIX 26. DETERMINATION OF THE
NUMBER OF IDEAL CLASSES IN THE CYCLOTOMIC FIELD OF THE M-TH ROOTS OF
UNITY 207 §116. THE SYMBOL J] 207 §117. THE EXPRESSION FOR THE CLASS
NUMBER OF THE CYCLOTOMIC FIELD OF THE M-TH ROOTS OF UNITY 208 §118.
DERIVATION OF THE EXPRESSIONS FOR THE CLASS NUMBER OF THE CYCLOTOMIC
FIELD FC(E 27RI / M ) 211 §119. THE EXISTENCE OF INFINITELY MANY
RATIONAL PRIMES WITH A PRESCRIBED RESIDUE MODULO A GIVEN NUMBER 213
§120. REPRESENTATION OF ALL THE UNITS OF THE CYCLOTOMIC FIELD BY
CYCLOTOMIC UNITS 215 27. APPLICATIONS OF THE THEORY OF CYCLOTOMIC FIELDS
TO QUADRATIC FIELDS 217 §121. GENERATION OF THE UNITS OF REAL QUADRATIC
FIELDS BY CYCLOTOMIC UNITS 217 §122. THE QUADRATIC RECIPROCITY LAW 217
§123. IMAGINARY QUADRATIC FIELDS WITH PRIME DISCRIMINANT 219 §124.
DETERMINATION OF THE SIGN OF THE GAUSS SUM 220 PART V. KUMMER NUMBER
FIELDS 28. FACTORISATION OF THE NUMBERS OF THE CYCLOTOMIC FIELD IN A
KUMMER FIELD 225 §125. DEFINITION OF KUMMER FIELDS 225 §126. THE
RELATIVE DISCRIMINANT OF A KUMMER FIELD 226 §127. THE SYMBOL {-} 229
§128. THE PRIME IDEALS OF A KUMMER FIELD 230 29. NORM RESIDUES AND
NON-RESIDUES OF A KUMMER FIELD 233 §129. DEFINITION OF NORM RESIDUES AND
NON-RESIDUES 233 §130. THEOREM ON THE NUMBER OF NORM RESIDUES.
RAMIFICATION IDEALS 233 §131. THE SYMBOL ( * ) 240 L RO J §132. SOME
LEMMAS ON THE SYMBOL -Y- AND NORM RESIDUES MODULO THE PRIME IDEAL [
243 §133. USE OF THE SYMBOL * * TO DISTINGUISH NORM RESIDUES AND
NON-RESIDUES 248 XX TABLE OF CONTENTS 30. EXISTENCE OF INFINITELY MANY
PRIME IDEALS WITH PRESCRIBED POWER CHARACTERS IN A KUMMER FIELD . 253
§134. THE LIMIT OF A CERTAIN INFINITE PRODUCT 253 §135. PRIME IDEALS OF
THE CYCLOTOMIC FIELD K(() WITH PRESCRIBED POWER CHARACTERS 254 31.
REGULAER CYCLOTOMIC FIELDS 257 §136. DEFINITION OF REGULAER CYCLOTOMIC
FIELDS, REGULAER PRIME NUMBERS AND REGULAER KUMMER FIELDS 257 §137. A
LEMMA ON THE DIVISIBILITY BY L OF THE FIRST FACTOR OF THE CLASS NUMBER
OF FC(E 27 "/') 257 §138. A LEMMA ON THE UNITS OF THE CYCLOTOMIC FIELD
K(E 2LTL/L ) WHEN / DOES NOT DIVIDE THE NUMERATORS OF THE FIRST \{L * 3)
BERNOULLI NUMBERS 259 §139. A CRITERION FOR REGULAER PRIME NUMBERS 262
§140. A SPECIAL INDEPENDENT SET OF UNITS IN A REGULAER CYCLOTOMIC FIELD
264 §141. A CHARACTERISTIC PROPERTY OF THE UNITS OF A REGULAER CYCLOTOMIC
FIELD 265 §142. PRIMARY NUMBERS IN REGULAER CYCLOTOMIC FIELDS 266 32.
AMBIG IDEAL CLASSES AND GENERA IN REGULAER KUMMER FIELDS 269 §143. UNIT
BUNDLES IN REGULAER CYCLOTOMIC FIELDS 269 §144. AMBIG IDEALS AND AMBIG
IDEAL CLASSES OF A REGULAER KUMMER FIELD 270 §145. CLASS BUNDLES IN
REGULAER KUMMER FIELDS 270 §146. TWO GENERAL LEMMAS ON FUNDAMENTAL SETS
OF RELATIVE UNITS OF A CYCLIC EXTENSION OF ODD PRIME NUMBER DEGREE 271
§147. IDEAL CLASSES DETERMINED BY AMBIG IDEALS 273 §148. THE SET OF ALL
AMBIG IDEAL CLASSES 280 §149. CHARACTER SETS OF NUMBERS AND IDEALS IN
REGULAER KUMMER FIELDS 282 §150. THE CHARACTER SET OF AN IDEAL CLASS AND
THE NOTION OF GENUS 284 §151. UPPER BOUND FOR THE DEGREE OF THE CLASS
BUENDLE OF ALL AMBIG CLASSES 285 §152. COMPLEXES IN A REGULAER KUMMER
FIELD 286 §153. AN UPPER BOUND FOR THE NUMBER OF GENERA IN A REGULAER
KUMMER FIELD 287 33. THE Z-TH POWER RECIPROCITY LAW IN REGULAER
CYCLOTOMIC FIELDS 289 §154. THE ^-TH POWER RECIPROCITY LAW AND THE
SUPPLEMENTARY LAWS . . 289 §155. PRIME IDEALS OF FIRST AND SECOND KIND
IN A REGULAER CYCLOTOMIC FIELD 290 TABLE OF CONTENTS XXI §156. LEMMAS ON
PRIME IDEALS OF THE FIRST KIND IN REGULAER CYCLOTOMIC FIELDS 293 §157. A
PARTICULAR CASE OF THE RECIPROCITY LAW FOR TWO IDEALS . 296 §158. THE
EXISTENCE OF CERTAIN AUXILIARY PRIME IDEALS FOR WHICH THE RECIPROCITY
LAW HOLDS 298 §159. PROOFOFTHE FIRST SUPPLEMENTARY LAW OFTHERECIPROCITY
LAW . 300 §160. PROOF OF THE RECIPROCITY LAW FOR ANY TWO PRIME IDEALS
. 301 §161. PROOF OF THE SECOND SUPPLEMENTARY LAW FOR THE RECIPROCITY
LAW 303 34. THE NUMBER OF GENERA IN A REGULAER KUMMER FIELD 305 §162. A
THEOREM ON THE SYMBOL J * } 305 §163. THE FUNDAMENTAL THEOREM ON THE
GENERA OF A REGULAER KUMMER FIELD 306 §164. THE CLASSES OF THE PRINCIPAL
GENUS IN A REGULAER KUMMER FIELD 308 §165. THEOREM ON THE RELATIVE NORMS
OF NUMBERS IN A REGULAER KUMMER FIELD 309 35. NEW FOUNDATION OF THE
THEORY OF REGULAER KUMMER FIELDS 313 §166. ESSENTIAL PROPERTIES OF THE
UNITS OF A REGULAER CYCLOTOMIC FIELD 313 §167. PROOF OF A PROPERTY OF
PRIMARY NUMBERS FOR PRIME IDEALS OF THE SECOND KIND 315 §168. PROOF OF
THE RECIPROCITY LAW WHERE ONE OF THE TWO PRIME IDEALS IS OF THE SECOND
KIND 318 §169. A LEMMA ABOUT THE PRODUCT JJ [ * J WHERE TU RUNS OVER ALL
PRIME IDEALS DISTINCT FROM [ 321 §170. THE SYMBOL {V, FX) AND THE
RECIPROCITY LAW BETWEEN ANY TWO PRIME IDEALS 324 §171. COINCIDENCE OF
THE SYMBOLS {V, SS} AND * ! * 325 36. THE DIOPHANTINE EQUATION A M +
SS M + -F 1 = 0 327 §172. THE IMPOSSIBILITY OF THE DIOPHANTINE EQUATION A
L + SS L + 7' = 0 FOR A REGULAER PRIME NUMBER EXPONENT L . . . 327 §173.
FURTHER INVESTIGATIONS ON THE IMPOSSIBILITY OF THE DIOPHANTINE EQUATION
A L + SS L + J L = 0 332 REFERENCES 335 LIST OF THEOREMS AND LEMMAS 345
INDEX 347 |
| any_adam_object | 1 |
| author | Hilbert, David 1862-1943 |
| author_GND | (DE-588)11855090X |
| author_facet | Hilbert, David 1862-1943 |
| author_role | aut |
| author_sort | Hilbert, David 1862-1943 |
| author_variant | d h dh |
| building | Verbundindex |
| bvnumber | BV012132508 |
| callnumber-first | Q - Science |
| callnumber-label | QA247 |
| callnumber-raw | QA247 |
| callnumber-search | QA247 |
| callnumber-sort | QA 3247 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SF 3940 SK 180 |
| ctrlnum | (OCoLC)39787283 (DE-599)BVBBV012132508 |
| 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 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| era | Geschichte 1897 gnd |
| era_facet | Geschichte 1897 |
| format | Book |
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| id | DE-604.BV012132508 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-20T11:03:22Z |
| institution | BVB |
| isbn | 3540627790 |
| language | German English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008217104 |
| oclc_num | 39787283 |
| open_access_boolean | |
| owner | DE-824 DE-83 DE-11 |
| owner_facet | DE-824 DE-83 DE-11 |
| physical | XXXVI, 350 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| spelling | Hilbert, David 1862-1943 Verfasser (DE-588)11855090X aut Die Theorie der algebraischen Zahlkörper The theory of algebraic number fields David Hilbert. Transl. from the German by Iain T. Adamson. With an introd. by Franz Lemmermeyer and Norbert Schappacher Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kon Springer 1998 XXXVI, 350 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 335 - 343 Geschichte 1897 gnd rswk-swf Algebraic fields Quelle (DE-588)4135952-5 gnd rswk-swf Algebraische Invariante (DE-588)4141838-4 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 s Geschichte 1897 z Quelle (DE-588)4135952-5 s DE-604 Algebraische Invariante (DE-588)4141838-4 s 1\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008217104&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hilbert, David 1862-1943 The theory of algebraic number fields Algebraic fields Quelle (DE-588)4135952-5 gnd Algebraische Invariante (DE-588)4141838-4 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd |
| subject_GND | (DE-588)4135952-5 (DE-588)4141838-4 (DE-588)4068537-8 |
| title | The theory of algebraic number fields |
| title_alt | Die Theorie der algebraischen Zahlkörper |
| title_auth | The theory of algebraic number fields |
| title_exact_search | The theory of algebraic number fields |
| title_full | The theory of algebraic number fields David Hilbert. Transl. from the German by Iain T. Adamson. With an introd. by Franz Lemmermeyer and Norbert Schappacher |
| title_fullStr | The theory of algebraic number fields David Hilbert. Transl. from the German by Iain T. Adamson. With an introd. by Franz Lemmermeyer and Norbert Schappacher |
| title_full_unstemmed | The theory of algebraic number fields David Hilbert. Transl. from the German by Iain T. Adamson. With an introd. by Franz Lemmermeyer and Norbert Schappacher |
| title_short | The theory of algebraic number fields |
| title_sort | the theory of algebraic number fields |
| topic | Algebraic fields Quelle (DE-588)4135952-5 gnd Algebraische Invariante (DE-588)4141838-4 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd |
| topic_facet | Algebraic fields Quelle Algebraische Invariante Algebraischer Zahlkörper |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008217104&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hilbertdavid dietheoriederalgebraischenzahlkorper AT hilbertdavid thetheoryofalgebraicnumberfields |