Let (R, m) be a local noetherian ring and let N \subseteq M
be two finitely generated R-modules such that the dim M/N \leq 1.
We give simple proof of the fact that there exists an integer h
such that I^n M \cap N = I^{n-h}(I^hM \cap N), for all n \geq h and for
all ideals I \subset R. We give upper bounds for such an integer h.
Moreover, we give two examples of rings of dimension two where
the property fails.
