2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58524The main object of this note is to study the conormal module $M$ and the computation of the second symbolic power $\bar I^{(2)}$ of an ideal $\bar I$ in the residue ring $R/H$ of a polynomial ring $R$ over a field of characteristic zero. The torsion part $T(M)$ of $M$ and the torsion free module $M/T(M)$ are expressed by the primitive ideal of $I$ relative to $H$. Two characterizations for $M/T(M)$ to be free are proved. Some immediate applications are worked out.11 pages, Latex2e fileAlgebraic GeometryCommutative AlgebraRings and Algebras13C12,14B07text