Exercise 29, § 2

Let $A$ be a commutative ring, $m$ an ideal of $A$ such that $\bigcap_{n > 0} m^n = 0$ and $c$ is an element of $A$ which is not a divisor of 0. Show that the transporters $q_n = m^n : Ac$ are open under the $m$-adic topology and have zero intersection. If $A$ is strictly linearly compact with the $m$-adic topology (Exercise 22(b)), $(q_n)$ is a fundamental system of neighbourhoods of 0 in $A$ for this topology.