with "K" the field of rational functions in the indeterminate "T" over the finite field with "p" elements. Here one can prove directly that "P"("X") is irreducible, and not separable. This is actually a typical example of why "inseparability" matters; in geometric terms "P" represents the mapping on the projective line over the finite field, taking co-ordinates to their "p"th power. Such mappings are fundamental to the algebraic geometry of finite fields. Put another way, there are coverings in that setting that cannot be 'seen' by Galois theory. (See radical morphism for a higher-level discussion.)