Questioni di suriettività di un morfismo canonico tra due complessi approssimati


In this paper, we introduce the concept of i-couple for two ideals, J,I, J\supseteq I, in a local noetherian ring (R,m).This concept is expressed in terms of the structure of H<sub>i</sub>(M) (where M is an approximation complex for the double Koszul complex L associated to the system of generators of J), and it generalizes the idea of (d,i)-sequence introduce in [M-R].We study the relationship between the following properties: 1) (J,I) is an i- couple of ideals in R; 2) \bar{J},\bar{I} is an i- couple of ideals in \bar{R}=R/I, more generally, in R/I', I'⊆ I.So we get some sufficient conditions for the "ascendent" and "descendent" properties of the i –couple.In particular, we study the surjectivity of the natural morphism(Error rendering LaTeX formula), since the surjectivity of \bar{φ}<sub>i</sub> is a sufficient condition for the "descendent" property of the i - ouple from R to \bar R.

DOI Code: 10.1285/i15900932v6n1p61

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