algebraic

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 algebraic over $F$.

For example, $\sqrt{2}\in ℝ$ is algebraic over$\mathbb{Q}$ since there is a nonzero polynomial with rationalcoefficients, namely $f(x)=x^2-2$, such that $f(\sqrt{2})=0$.

If all elements of $K$ are algebraic over $F$, one says thatthe field extension $K/F$ is algebraic.