product of a module with the ideal

Let \(R\) be a ring, \(M\) an \(R\)-module and \(\mathfrak{a} \subseteq R\) an ideal. Then the <modulideal> \(\mathfrak{a}M \subseteq\) (besserer name bitte ?) is defined as submodule

\begin{align*} \mathfrak{a}M \coloneqq \{a \cdot m \vert a \in \mathfrak{a}, m \in M\} \end{align*}

follows from <Kriterium für ein Untermodul> and definition of an ideal