Example 2

Let $A$ be a ring and let $\mathfrak{B}$ be a filter base on $A$ consisting of two-sided ideals of $A$; let $E$ be a left $A$-module. If we give $A$ the topology (compatible with its ring structure) for which $\mathfrak{B}$ is a fundamental system of neighbourhoods of $0$ (no. 3, Example 3), and $E$ the topology (compatible with its additive group structure) in which the sets $aE$, as $a$ runs through $\mathfrak{B}$, form a fundamental system of neighbourhoods of $0$ ($§ 1$, no. 2, Example), it is immediately verified that $E$ is a topological $A$-module.