This ratio is a certain algebraic number of degree 4.

His early research concerned various properties and structures of algebraic numbers.

The reason for this distinction relates to general algebraic number theory.

This question is of special interest if is an algebraic number.

A separate inspiration for F came from algebraic number theory.

Therefore, elements of F are also referred to as algebraic numbers.

Class field theory is the key part and the heart of algebraic number theory.

Almost any book on modern algebraic number theory, such as:

For more information about that: read algebraic number theory.

He is known for his work in the areas of automorphic forms, and algebraic number theory.

He took up Waring's problem in algebraic number fields and got interesting results.

He was of the opinion that I must publish the thing at least in so far as it concerns the algebraic numbers.

In algebraic number theory one defines also norms for ideals.

An algebraic number of degree 1 is a rational number.

This is one of the main results of classical algebraic number theory.

A real algebraic number of degree 2 is a quadratic irrational.

Another example, playing a key role in algebraic number theory, is the field Q of p-adic numbers.

Other books of his covered projective geometry and algebraic number theory.

Cantor showed that the set of algebraic numbers is countable.

The totally real number fields play a significant special role in algebraic number theory.

Important examples of locally profinite groups come from algebraic number theory.

If we set up a definite listing of all algebraic numbers .

His other interests included algebraic number theory, mathematical economics and geometry of numbers.

The field of real algebraic numbers is a Euclidean field.

By the going-down result above, no algebraic number field can be Euclidean.