Generating set of a module

Let \(R\) be a ring and \(M\) a left $R$-module. A subset \(S\subseteq M\) is a generating set for \(M\) if every \(x\in M\) is a finite \(R\)-linear combination of elements of \(S\): there exist \(n\geq 0\), \(s_1,\ldots,s_n\in S\), and \(r_1,\ldots,r_n\in R\) with \(x = \sum_{i=1}^n r_i s_i\).