Sold Out
Book Categories |
Translator's Preface | ||
Hilbert's Preface | ||
Introduction to the English Edition | ||
Pt. I | The Theory of General Number Fields | |
1 | Algebraic Numbers and Number Fields | 3 |
2 | Ideals of Number Fields | 9 |
3 | Congruences with Respect to Ideals | 17 |
4 | The Discriminant of a Field and its Divisors | 25 |
5 | Extension Fields | 33 |
6 | Units of a Field | 41 |
7 | Ideal Classes of a Field | 53 |
8 | Reducible Forms of a Field | 65 |
9 | Orders in a Field | 67 |
Pt. II | Galois Number Fields | |
10 | Prime Ideals of a Galois Number Field and its Subfields | 79 |
11 | The Differents and Discriminants of a Galois Number Field and its Subfields | 89 |
12 | Connexion Between the Arithmetic and Algebraic Properties of a Galois Number Field | 93 |
13 | Composition of Number Fields | 97 |
14 | The Prime Ideals of Degree 1 and the Class Concept | 101 |
15 | Cyclic Extension Fields of Prime Degree | 105 |
Pt. III | Quadratic Number Fields | |
16 | Factorisation of Numbers in Quadratic Fields | 115 |
17 | Genera in Quadratic Fields and Their Character Sets | 121 |
18 | Existence of Genera in Quadratic Fields | 133 |
19 | Determination of the Number of Ideal Classes of a Quadratic Field | 149 |
20 | Orders and Modules of Quadratic Fields | 155 |
Pt. IV | Cyclotomic Fields | |
21 | The Roots of Unity with Prime Number Exponent l and the Cyclotomic Field They Generate | 161 |
22 | The Roots of Unity for a Composite Exponent m and the Cyclotomic Field They Generate | 167 |
23 | Cyclotomic Fields as Abelian Fields | 175 |
24 | The Root Numbers of the Cyclotomic Field of the l-th Roots of Unity | 187 |
25 | The Reciprocity Law for l-th Power Residues Between a Rational Number and a Number in the Field of l-th Roots of Unity | 199 |
26 | Determination of the Number of Ideal Classes in the Cyclotomic Field of the m-th Roots of Unity | 207 |
27 | Applications of the Theory of Cyclotomic Fields to Quadratic Fields | 217 |
Pt. V | Kummer Number Fields | |
28 | Factorisation of the Numbers of the Cyclotomic Field in a Kummer Field | 225 |
29 | Norm Residues and Non-residues of a Kummer Field | 233 |
30 | Existence of Infinitely Many Prime Ideals with Prescribed Power Characters in a Kummer Field | 253 |
31 | Regular Cyclotomic Fields | 257 |
32 | Ambig Ideal Classes and Genera in Regular Kummer Fields | 269 |
33 | The l-th Power Reciprocity Law in Regular Cyclotomic Fields | 289 |
34 | The Number of Genera in a Regular Kummer Field | 305 |
35 | New Foundation of the Theory of Regular Kummer Fields | 313 |
36 | The Diophantine Equation [alpha][superscript m] + [beta][superscript m] + [gamma][superscript m] = 0 | 327 |
References | 335 | |
List of Theorems and Lemmas | 345 | |
Index | 347 |
Login|Complaints|Blog|Games|Digital Media|Souls|Obituary|Contact Us|FAQ
CAN'T FIND WHAT YOU'RE LOOKING FOR? CLICK HERE!!! X
You must be logged in to add to WishlistX
This item is in your Wish ListX
This item is in your CollectionThe Theory of Algebraic Number Fields
X
This Item is in Your InventoryThe Theory of Algebraic Number Fields
X
You must be logged in to review the productsX
X
X
Add The Theory of Algebraic Number Fields, This book is a translation into English of Hilbert's Theorie der algebraischen Zahlkorper, best known as the Zahlbericht, first published in 1897, in which he provided an elegantly integrated overview of the development of algebraic number theory up to th, The Theory of Algebraic Number Fields to the inventory that you are selling on WonderClubX
X
Add The Theory of Algebraic Number Fields, This book is a translation into English of Hilbert's Theorie der algebraischen Zahlkorper, best known as the Zahlbericht, first published in 1897, in which he provided an elegantly integrated overview of the development of algebraic number theory up to th, The Theory of Algebraic Number Fields to your collection on WonderClub |