Definition 10.11.2. Let $R$ be a ring. Let $M$ be an $R$-module. Let $n \geq 0$ and $x_ i \in M$ for $i = 1, \ldots , n$. A *relation* between $x_1, \ldots , x_ n$ in $M$ is a sequence of elements $f_1, \ldots , f_ n \in R$ such that $\sum _{i = 1, \ldots , n} f_ i x_ i = 0$.

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