Let $R$ be a ring, $L$ an $R$-module, and ${\ell_i}_{i\in I}$ a subset of $L$. The submodule generated by the $\ell_i$ is the set \(\left\{\sum_{i=1}^n a_i\ell_i\mid a_i\in R, \text{ all but finitely many } a_i=0\right\}.\) Equivalently, it is the smallest submodule of $L$ containing the $\ell_i$.
Wikidata ID: Q25106477