If is an -scheme and the Frobenius morphism of is the identity, then the absolute Frobenius morphism is a morphism of -schemes. In general, however, it is not. For example, consider the ring formula_18. Let and both equal with the structure map being the identity. The Frobenius morphism on sends to . It is not a morphism of formula_19-algebras. If it were, then multiplying by an element in formula_19 would commute with applying the Frobenius endomorphism. But this is not true because: