Questioni di suriettività di un morfismo canonico tra due complessi approssimati

Abstract

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 $H_i(M)$ (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 $\bar{φ}₁:H₁(M)→H₁(\bar{M})$, since the surjectivity of $\bar{φ}_i$ is a sufficient condition for the "descendent" property of the i - ouple from R to $\bar R$.