Abstract: | Summary In this paper we define quasi étale ring homomorphisms, as a generalization of étale ones, and we show that if ϕ: A→B is a
quasi étale homomorphism of noetherian rings, and A is excellent, then B is excellent. The converse is not always true; however
we show that if ϕ is faithfully flat and regular (in particular qnasi étale), if A is universally catenarian and B is excellent,
then A is excellent. The above statements can be applied when B is the henselization of A with respect to an ideal; and from
this it follows that a Hensel pair is a direct limit of excellent ones.
Lavoro eseguito nell’ambito del Comitato Nazionale per la Matematica del C.N.R.
Entrata in Redazione il 25 Febbraio 1971. |