Let \(R\) be a ring and \(M\) an \(R\)-module and \(S \subseteq M\) a subset
Then \(S\) is said to generate \(M\), if
\begin{align*}
\langle S\rangle = M
\end{align*}
i.e. each element \(m\) of \(M\) is a finite sum
\begin{align*}
m = \sum \alpha_i s_i
\end{align*}