Sur l’unicité de la forme des factorisations de longueur maximale d’une extension purement inséparable finie

Let K/k be a finite purely inseparable extension of field k of characteristic p > 0. A factorization of length m of K/k is the data of m intermediate fields K₁,K₂, ··· ,Km of K/k such as K ≃ K₁ ⊗_k K₂ ⊗_k ···⊗_k Km. In the present paper, we are especially interested in the uniqueness of the form of factorizations of maximum length.