2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101289The 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.This is a new version (28 pages) which is accepted for publication in Bull. Soc. Math. France (2006)Algebraic GeometryComplex Variables32 S 05, 32 S 25, 32 S 40text