Algebraic Number TheorySpringer Science & Business Media, 6 dic 2012 - 269 pagine From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995 |
Dall'interno del libro
Pagina 1
... Unique Factorization in Prime Elements 2.2 . The Concept of a Domain with Divisor Theory 2222 21 23 2.3 . Divisor Theory for the Maximal Order of an Algebraic Number Field 25 §3 . Dedekind Rings 27 3.1 . Definition of Dedekind Rings 3.2 ...
... Unique Factorization in Prime Elements 2.2 . The Concept of a Domain with Divisor Theory 2222 21 23 2.3 . Divisor Theory for the Maximal Order of an Algebraic Number Field 25 §3 . Dedekind Rings 27 3.1 . Definition of Dedekind Rings 3.2 ...
Pagina 8
... unique factorization in prime numbers , Kummer introduced " ideal numbers " and showed the unique factorization in ideal prime numbers . With this concept he was able to prove Fermat's last theorem in many new cases using the identity x ...
... unique factorization in prime numbers , Kummer introduced " ideal numbers " and showed the unique factorization in ideal prime numbers . With this concept he was able to prove Fermat's last theorem in many new cases using the identity x ...
Pagina 9
... unique factorization of natural numbers in the product of prime numbers . The arithmetic in Q is given by the arithmetic in Z : Any re Q - { 0 } has a uniquely determined representation r = ( − 1 ) ˇ [ ] p3 » ( r ) P where the product ...
... unique factorization of natural numbers in the product of prime numbers . The arithmetic in Q is given by the arithmetic in Z : Any re Q - { 0 } has a uniquely determined representation r = ( − 1 ) ˇ [ ] p3 » ( r ) P where the product ...
Pagina 12
... unique square free de Z such that K = Q ( √d ) . Let @ = [ ( 1 + √d ) / 2 Wa ifd = 1 ( mod 4 ) if d = 2 , 3 ( mod ... uniquely determined by its in discriminant . This is not true in general for fields of higher degree ( Example 19 ) ...
... unique square free de Z such that K = Q ( √d ) . Let @ = [ ( 1 + √d ) / 2 Wa ifd = 1 ( mod 4 ) if d = 2 , 3 ( mod ... uniquely determined by its in discriminant . This is not true in general for fields of higher degree ( Example 19 ) ...
Pagina 18
... unique fundamental unit of O , with & > 1 . ( Hasse Example 5. K = Q ( √√ / 5 ) , ƒ = 1. Then a = ( 1 + √√5 ) / 2 is reduced and α = [ i ] . Therefore 91 1 , ε = α . - Example 6. K = Q ( √ / 19 ) , ƒ = 1 , x = ( √ / 19 – 4 ) 1 ...
... unique fundamental unit of O , with & > 1 . ( Hasse Example 5. K = Q ( √√ / 5 ) , ƒ = 1. Then a = ( 1 + √√5 ) / 2 is reduced and α = [ i ] . Therefore 91 1 , ε = α . - Example 6. K = Q ( √ / 19 ) , ƒ = 1 , x = ( √ / 19 – 4 ) 1 ...
Sommario
7 | |
22 | |
3 Dedekind Rings | 28 |
60 | 42 |
69 | 49 |
76 | 56 |
Harmonic Analysis on Local and Global Fields | 63 |
6 Hecke LSeries and the Distribution of Prime Ideals | 70 |
7 Further Results of Class Field Theory | 145 |
Cohomology of Profinite Groups | 151 |
2 Galois Cohomology of Local and Global Fields | 168 |
Abelian Fields | 192 |
3 Iwasawas Theory of IExtensions | 206 |
Artin LFunctions and Galois Module Structure | 219 |
2 Galois Module Structure and Artin Root Numbers | 234 |
Fields Domains and Complexes | 237 |
Class Field Theory | 90 |
2 Complex Multiplication | 107 |
Simple Algebras | 131 |
6 Explicit Reciprocity Laws and Symbols | 137 |
Tables | 245 |
References | 251 |
Author Index 263 | 262 |
Altre edizioni - Visualizza tutto
Parole e frasi comuni
a₁ abelian extension abelian field abelian group algebraic number field arbitrary Artin automorphism called Chap class field theory closed subgroup cohomology complex conductor conjecture corresponding cyclic Dedekind ring defined denotes Dirichlet discriminant divisor theory exact sequence Example extension L/K extension of Q finite extension finite group finite normal extension following theorem function G-module G₁ Galois group global fields group G H¹(G H²(G Hasse Hecke character Hence Hilbert homomorphism ideal class group idele imaginary-quadratic implies induces infinite places integers irreducible isomorphism L-functions Lemma Let G Let L/K Main reference module morphism natural number norm symbol normal extension normal subgroup number theory polynomial prime divisors prime element prime ideal prime numbers principal ideal pro-p-group profinite group Proposition quadratic r₂ ramified reciprocity law representation resp roots of unity Shafarevich simple algebra subgroup of G trivial U₁ unramified valuation Z/pZ