Definition:Generator of Module

Definition
Let $R$ be a ring.

Let $M$ be an $R$-module.

Let $S \subseteq M$ be a subset.

Generated Submodule
Let $R$ be a ring.

Let $M$ be an $R$-module.

Let $S \subseteq M$ be a subset.

Also see

 * Equivalence of Definitions of Generator of Module
 * Equivalence of Definitions of Generator of Module over Ring with Unity