Category:Definitions/Generators of Modules
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This category contains definitions related to Generators of Modules.
Related results can be found in Category: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 $S$.
Pages in category "Definitions/Generators of Modules"
The following 16 pages are in this category, out of 16 total.
G
- Definition:Generated Module
- Definition:Generated Submodule
- Definition:Generated Submodule/Definition 1
- Definition:Generated Submodule/Unitary
- Definition:Generating Set of Module
- Definition:Generating System of Module
- Definition:Generator for Module
- Definition:Generator of Module
- Definition:Generator of Module/Also known as
- Definition:Generator of Module/Definition 1
- Definition:Generator of Module/Definition 2
- Definition:Generator of Module/Unitary
- Definition:Generator of Unitary Module