 For example, formula_30 is algebraic over the rational numbers, because it is a root of formula_31 If an element "x" of "L" is algebraic over "K", the monic polynomial of lowest degree that has "x" as a root is called the minimal polynomial of "x".This minimal polynomial is irreducible over "K".An element "s" of "L" is algebraic over "K" if and only if the simple extension is a finite extension.