Proposition 4

— Let $K$ be a field of characteristic exponent q. For every integer $f \geq 0$ the mapping $x \mapsto x^{q^f}$ is an isomorphism of K on one of its subfields (denoted by $K^{q^f}$). This follows from Th. 2 when q ≠ 1 and is trivial when q = 1. Likewise one can extend Prop. 2 to the case where $A$ is a field of characteristic exponent q, the case q = 1 being trivial.