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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...

class field, the maximal abelian unramified extension of a number field Hilbert–Speiser field, a field with a normal integral basis Hilbertian field,...

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...

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)...

Hilbert ring Hilbert–Poincaré series Hilbert series and Hilbert polynomial Hilbert space Hilbert spectrum Hilbert system Hilbert transform Hilbert's arithmetic...

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...

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...

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...

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...

In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional)...

module Galois cohomology Brauer group Class field theory Abelian extension Kronecker–Weber theorem Hilbert class field Takagi existence theorem Hasse norm...

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...

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...

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...

though Hilbert may have implicitly meant to include these. More seriously, while values of elliptic modular functions generate the Hilbert class field, for...

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...

Hilbert symbol. 1897 Kurt Hensel introduced p-adic numbers. 1898 Hilbert conjectures the existence and properties of the (narrow) Hilbert class field...

the class of bounded operators considered or by specifying a particular class of Banach spaces. The problem is still open for separable Hilbert spaces...

discriminant Δ = − 31 {\displaystyle \Delta =-31} . The Hilbert class field of imaginary quadratic field K = Q ( Δ ) {\displaystyle K=\mathbb {Q} ({\sqrt {\Delta...

Einstein–Hilbert equations Hilbert algebra Hilbert C*-module Hilbert basis (linear programming) Hilbert class field Hilbert cube Hilbert curve Hilbert curve...