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Homedegree of an algebraic number

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# degree of an algebraic number

Let $\alpha$ be an algebraic number. The *degree* of $\alpha$ is the degree of the minimal polynomial for $\alpha$ over $\mathbb{Q}$.

In a similar 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 $\deg\sqrt[3]{2}=3$.

Related:

AlgebraicNumber, Degree8, MinimalPolynomial, TheoryOfAlgebraicNumbers

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

12E05*no label found*12F05

*no label found*11C08

*no label found*11R04

*no label found*

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