Sugli omomorfismi quasi étale e gli anelli eccellenti

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.

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Lavoro eseguito nell’ambito del Comitato Nazionale per la Matematica del C.N.R.

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Entrata in Redazione il 25 Febbraio 1971.