  The aim of this fisrt part is to introduce, for a rather large class of
hypersurface singularities with 1 dimensionnal locus, the analog of the
Brieskorn lattice at the origin (the singular point of the singular locus). The
main results are the finitness theorem for the corresponding (a,b)-module
obtained via Kashiwara's constructibility theorem, and non torsion results for
a plane curve singularity (not nessarily reduced) and for the suspension of
such non torsion cases with an isolated singularity.
