Corollary

— Let L be a p-radical extension of height $\leq 1$ of K and M a subextension of L. Then L is p-radical of height $\leq 1$ over M and M is p-radical of height $\leq 1$ over K. Moreover, if B is a p-basis of M over K and C is a p-basis of L over M, then $B \cap C = \varnothing$ and $B \cup C$ is a p-basis of L over K.

Let K be a field. A family $(x_i)_{i \in I}$, is said to be a (absolute) p-basis of K if it is a p-basis of K over $K^p$. For every integer $n \geq 1$ we denote by $\Lambda(n)$ the subset of $N^{(I)}$ consisting of all $a = (\alpha_i)_{i \in I}$, such that $\alpha_i < p^n$ for all $i \in I$.