linearly independent

Let \(R\) be a commutative ring, \(M\) a \(R\)-module and \(S \subseteq M\) a subset.
Then \(S\) is linearly independent, if for a linear combination with \(r_i \in R, m_i \in S\)

\begin{align*} \sum_{i=1}^{n} r_i m_i = 0 \Rightarrow r_i = 0 \end{align*}