 Equivalently, an algebraic extension is an extension that is generated by algebraic elements.For example, formula_33 is an algebraic extension of formula_23, because formula_30 and formula_36 are algebraic over formula_9

A simple extension is algebraic if and only if it is finite.This implies that an extension is algebraic if and only if it is the union of its finite subextensions, and that every finite extension is algebraic.