PlanetMath: algebraic number

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algebraic number

(Definition)

A number $\alpha \in \mathbb{C}$ is called an algebraic number if there exists a polynomial $f(x) = a_n x^n + \cdots + a_0$ such that $a_0, \ldots , a_n$ , not all zero, are in $\mathbb{Q}$ and $f(\alpha )=0$ .

"algebraic number" is owned by KimJ.

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Keywords:

algebraic number theory

Attachments:: algebraic numbers are countable (Theorem) by pahio
norm and trace of algebraic number (Theorem) by pahio
multiples of an algebraic number (Theorem) by pahio

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Cross-references: polynomial
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This is version 5 of algebraic number, born on 2001-10-15, modified 2006-10-26.
Object id is 209, canonical name is AlgebraicNumber.
Accessed 7039 times total.

Classification:

AMS MSC:

11R04 (Number theory :: Algebraic number theory: global fields :: Algebraic numbers; rings of algebraic integers)

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