Example 5

Let us take up again the hypotheses and notations of Example 1. Then $T(A/\mathfrak{m}_A^n) = \mathrm{Hom}_A(A/\mathfrak{m}_A^n, J)$ is identified with the submodule $J_n$ of $J$ formed by the elements annihilated by $\mathfrak{m}_A^n$; by passing to the inductive limit one obtains a canonical isomorphism of $I$ onto $J$.