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- theory, the Hilbert class field E of a number field K is the maximal abelian unramified extension of K. Its degree over K equals the class number of K...7 KB (920 words) - 20:19, 21 October 2021
- class field, the maximal abelian unramified extension of a number field Hilbert–Speiser field, a field with a normal integral basis Hilbertian field,...413 bytes (89 words) - 19:52, 26 April 2013
- the Hilbert class field of a number field, which can be defined as the maximal unramified abelian extension of such a field. The Hilbert class field L of...14 KB (2,148 words) - 23:16, 3 August 2024
- defined in terms of the Artin symbol of local class field theory. The Hilbert symbol was introduced by David Hilbert (1897, sections 64, 131, 1998, English translation)...11 KB (1,571 words) - 14:55, 23 June 2024
- Hilbert ring Hilbert–Poincaré series Hilbert series and Hilbert polynomial Hilbert space Hilbert spectrum Hilbert system Hilbert transform Hilbert's arithmetic...58 KB (6,933 words) - 06:56, 20 August 2024
- Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several...40 KB (3,673 words) - 05:17, 14 August 2024
- extended to an ideal of the Hilbert class field. This means that there is an element of the ring of integers of the Hilbert class field, which is an ideal number...7 KB (1,226 words) - 12:05, 8 November 2023
- Algebraic number theory (section Hilbert)class field theory. The concepts were highly influential, and his own contribution lives on in the names of the Hilbert class field and of the Hilbert symbol...40 KB (5,798 words) - 13:01, 5 July 2024
- an algebraic number field to the class group of its Hilbert class field, which sends all ideal classes to the class of a principal ideal. The phenomenon...4 KB (372 words) - 02:14, 16 December 2022
- In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional)...128 KB (17,487 words) - 22:34, 20 June 2024
- module Galois cohomology Brauer group Class field theory Abelian extension Kronecker–Weber theorem Hilbert class field Takagi existence theorem Hasse norm...2 KB (187 words) - 23:15, 29 June 2024
- Takagi existence theorem (redirect from Generalized ideal class group)Hilbert class field, not true of smaller abelian extensions of a number field, is that all ideals in a number field become principal in the Hilbert class...6 KB (828 words) - 16:32, 14 July 2024
- local and global fields using objects associated to the ground field. Hilbert is credited as one of pioneers of the notion of a class field. However, this...16 KB (2,212 words) - 16:30, 14 July 2024
- quadratic field K = Q ( Δ ) {\displaystyle K=\mathbb {Q} ({\sqrt {\Delta }})} has class number h = 3. {\displaystyle h=3.} Thus, the Hilbert class field of...16 KB (2,734 words) - 15:50, 14 July 2024
- though Hilbert may have implicitly meant to include these. More seriously, while values of elliptic modular functions generate the Hilbert class field, for...9 KB (1,185 words) - 01:38, 27 May 2024
- The Hilbert class field is the ray class field corresponding to the unit ideal and the empty set of real places, so it is the smallest ray class field. The...5 KB (773 words) - 00:30, 23 May 2023
- Hilbert symbol. 1897 Kurt Hensel introduced p-adic numbers. 1898 Hilbert conjectures the existence and properties of the (narrow) Hilbert class field...5 KB (561 words) - 01:56, 12 August 2023
- the class of bounded operators considered or by specifying a particular class of Banach spaces. The problem is still open for separable Hilbert spaces...17 KB (2,208 words) - 21:48, 20 August 2024
- discriminant Δ = − 31 {\displaystyle \Delta =-31} . The Hilbert class field of imaginary quadratic field K = Q ( Δ ) {\displaystyle K=\mathbb {Q} ({\sqrt {\Delta...16 KB (2,664 words) - 03:11, 14 July 2024
- Einstein–Hilbert equations Hilbert algebra Hilbert C*-module Hilbert basis (linear programming) Hilbert class field Hilbert cube Hilbert curve Hilbert curve...3 KB (225 words) - 14:55, 4 April 2022
- David Hilbert (January 23, 1862 – February 14, 1943) was a German logician, mathematician, and mathematical physicist. He is recognized as one of the
- Mathematical Problems (1900) by David Hilbert 949877Mathematical Problems1900David Hilbert Mathematical Problems Lecture delivered before the International
- 24.6 (Hilbert's Nullstellensatz, weak form): Let F = F ¯ {\displaystyle \mathbb {F} ={\overline {\mathbb {F} }}} be an algebraically closed field. For