degree of an algebraic number

Let $\alpha$ be an algebraic number. The degree of $\alpha$ is the degree (http://planetmath.org/Degree8) of the minimal polynomial for $\alpha$ over $\mathbb{Q}$.

In a manner to polynomials, the degree of $\alpha$ may be denoted $\mathrm{deg}\alpha$.

For example, since $x^3-2$ is the minimal polynomial for $\sqrt[3]{2}$ over $\mathbb{Q}$, we have $\mathrm{deg}\sqrt[3]{2}=3$.

Title	degree of an algebraic number
Canonical name	DegreeOfAnAlgebraicNumber
Date of creation	2013-03-22 17:50:05
Last modified on	2013-03-22 17:50:05
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	4
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 12E05
Classification	msc 12F05
Classification	msc 11C08
Classification	msc 11R04
Related topic	AlgebraicNumber
Related topic	Degree8
Related topic	MinimalPolynomial
Related topic	TheoryOfAlgebraicNumbers