An algebraic extension L/K is called simple if L=K(𝛼) for some 𝛼∈L. The element 𝛼 is called a primitive element for L/K. Every finite separable algebraic field extension is simple.

Suppose that L=K(𝛼₁,…𝛼ᵣ) is a finite separable extension and K_0⊆K is an infinite subset of K. Then there exists a primitive element 𝛼 of the form 𝛼=∑ᵢ₌₁ʳc_i𝛼ᵢ with c_i∈K_0.