Generating set of a module
= Generating set of a module
{title2=$M=\sum_{s\in S}Rs$}
= Generating sets of a module
{synonym}
A subset $S$ of a <module> $M$ generates $M$ when every element of $M$ is a finite sum $\sum_{s\in S}r_ss$, with coefficients in the scalar <ring>. The existence of a finite such subset defines a <finitely generated module>.