# 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 $\deg\alpha$.

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

 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