Definition:Algebraic Number

Definition
An algebraic number is an algebraic element of the field extension $\C / \Q$.

That is, it is a complex number that is a root of a polynomial with rational coefficients.

The set of algebraic number can often be seen denoted as $\mathbb A$.

Algebraic Number over Field
Some sources define an algebraic number over a more general field:

Also see

 * Definition:Algebraic Integer
 * Rational Number is Algebraic
 * Definition:Algebraic Element of Field Extension