The conormal module of an almost complete intersection

Abstract:

The conormal module of an ideal I in a commutative ring S is the $S/I$-module $I/{I^2}$. Assume S is a regular noetherian ring and I a prime ideal, which is locally everywhere a complete intersection or an almost complete intersection (i.e. needs one generator more than in the complete intersection case). In this situation necessary and sufficient conditions for $I/{I^2}$ being torsion free are given. Moreover the torsion of $I/{I^2}$ is expressed in terms of Kähler differentials of $S/I$.