## Number Field

If is an Algebraic Number of degree , then the totality of all expressions that can be constructed from by repeated additions, subtractions, multiplications, and divisions is called a number field (or an Algebraic Number Field) generated by , and is denoted . Formally, a number field is a finite extension of the Field of Rational Numbers.

The numbers of a number field which are Roots of a Polynomial

with integral coefficients and leading coefficient 1 are called the Algebraic Integers of that field.