\begin{definition}[Definition:Generator of Module/Also known as]
A '''generator''' of a module is also known as a '''spanning set'''.
Some sources refer to a '''generator for''' rather than '''generator of'''. The two terms mean the same.
It can also be said that $S$ '''generates $M$ (over $R$)'''.
Other terms for $S$ are:
* A '''generating set of $M$ (over $R$)'''
* A '''generating system of $M$ (over $R$)'''
Some sources refer to such an $S$ as a '''set of generators of $M$ over $R$''' but this terminology is misleading, as it can be interpreted to mean that each of the elements of $S$ is itself a '''generator''' of $M$ independently of the other elements.
Category:Definitions/Generators of Modules
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Prime.mover
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\end{definition}