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 S/I -module I / I 2 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 I/{I^2} being torsion free are given. Moreover the torsion of I / I 2 I/{I^2} is expressed in terms of Kähler differentials of S / I S/I .