algebraicAlgebraicElement2001-11-08 00:58:212002-05-30 21:59:22Definition\usepackage{amssymb}
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\usepackage{xypic}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 \emph{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 $f(\sqrt{2})=0$.