Generalization of the $${\varvec{lq}}$$lq-modular closure theorem and applications

Archiv der Mathematik - Let k be a field of characteristic $$ p\not =0 $$. For a (purely) inseparable extension K / k the notion of modularity, defined by M.E. Sweedler in the...     

Sur les extensions purement inséparables

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.Received: 4 April 2002