Sur les extensions purement inséparables

Abstract.

If K/k is a finite purely inseparable extension of fields, we are interested in the factorizations of K as a tensor product over k of intermediates fields of K/k. We introduce the notion of e-factorization that generalizes the notion of modular factorization. Contrary to modular factorization, K/k has always an e-factorization and its factors, when their number is maximum, are quasi-invariants.