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Let $K$ be an extension field of $F$ and let $a\in K$
If there is a nonzero polynomial $f\in F[x]$ such that $f(a)=0$ (in $K$ we say that $a$ is <</SPAN>#49#>algebraic over $F$ .
For example, $\sqrt{2}\in\mathbb{R}$ is algebraic over $\mathbb{Q}$ since there is a nonzero polynomial with rational coefficients, namely $f(x)=x^2-2$ such that $f(\sqrt{2})=0$
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"algebraic" is owned by drini. [ owner history (1) ]
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Cross-references: coefficients, rational, polynomial, extension field
There are 129 references to this entry.
This is version 3 of algebraic, born on 2001-11-08, modified 2002-05-30.
Object id is 705, canonical name is AlgebraicElement.
Accessed 9033 times total.
Classification:
| AMS MSC: | 13B05 (Commutative rings and algebras :: Ring extensions and related topics :: Galois theory) | | | 11R04 (Number theory :: Algebraic number theory: global fields :: Algebraic numbers; rings of algebraic integers) | | | 11R32 (Number theory :: Algebraic number theory: global fields :: Galois theory) |
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Pending Errata and Addenda
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