Dedekind Different and Type Sequence

Let R be a one-dimensional, local, Noetherian domain. We assume R anali-tycally irreducible and residually rational. Let ω be a canonical module of R such that R ⊆ ω ⊆ R and let θD: = R: ω be the Dedekind different of R. Our purpose is to study how θD is involved in the type sequence of R and to compare the type sequence of R with the type sequence of θD (for the notion of type sequence we refer to [11], [1] and [13]). These relations yield some interesting consequences.