Category:Generators of Modules

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This category contains results about Generators of Modules.
Definitions specific to this category can be found in Definitions/Generators of Modules.

Let $R$ be a ring.

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

Let $S \subseteq M$ be a subset.


Definition 1

$S$ is a generator of $M$ if and only if $M$ is the submodule generated by $S$.


Definition 2

$S$ is a generator of $M$ if and only if $M$ has no proper submodule containing $S$.