Search Results for ""

A totally imaginary field is a field with no real embeddings. A general number field K of degree n has s real embeddings (0<=s<=n) and 2t imaginary embeddings (0<=t<=n/2), ...

A place nu of a number field k is an isomorphism class of field maps k onto a dense subfield of a nondiscrete locally compact field k_nu. In the function field case, let F be ...

A finite field is a field with a finite field order (i.e., number of elements), also called a Galois field. The order of a finite field is always a prime or a power of a ...

The algebraic integers in a number field.

Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...

A sieving procedure that can be used in conjunction with Dixon's factorization method to factor large numbers n. Pick values of r given by r=|_sqrt(n)_|+k, (1) where k=1, 2, ...

A perfect field is a field F such that every algebraic extension is separable. Any field in field characteristic zero, such as the rationals or the p-adics, or any finite ...

A prime field is a finite field GF(p) for p is prime.

The study of number fields by embedding them in a local field is called local class field theory. Information about an equation in a local field may give information about ...

Given a ring R with identity, the general linear group GL_n(R) is the group of n×n invertible matrices with elements in R. The general linear group GL_n(q) is the set of n×n ...