Anneaux de valuation discrète et modules des différentielles

The module of Kähler differentials of a commutativeG-algebraXis essentially described by two cardinals and two integers whenXis a valuation ring and when the residue extension is good enough. The first cardinal and the two integers have been described by R. Berger and E. Kunz. The last cardinal deals with the divisible part of the torsion of the module of differentials. It is proved to be finite and given by an equality involving the Krull dimension and the module of imperfection.