Divisors of a module and blow up

In this paper we work with several divisors of a module E⊆G≃Re having rank e, such as the classical Fitting ideals of E and of G/E, and the more recently introduced (generic) Bourbaki ideals I(E) (Simis et al. (2003) [19], ) or ideal norms [[E]]R (Villamayor (2006) [23], ). We found several relations and equalities among them which allow to describe in some cases universal properties with respect to E of their blow ups. As a byproduct we are also able to obtain lower bounds for the analytic spread ℓ(⋀eE), related with the algebraic local version of Zak’s inequality as explained in Simis et al. (2002) [17].