Definition 1

Let A be a commutative ring and $\mathfrak{g}$ an ideal of A. An A-module M is called ideally Hausdorff with respect to 3 (or simply ideally Hausdorff if there is no ambiguity) if, for every finitely generated ideal $\mathfrak{a}$ of A, the A-module $\mathfrak{a} \otimes_A M$ is Hausdorff with the 3-adic topology.

Putting $\mathfrak{a} = A$ in this definition, we have already seen that M is necessarily Hausdorff with the 3-adic topology.

Examples