# Definition:Generator

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## Disambiguation

This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

**Generator** may refer to:

- Abstract Algebra:
- Definition:Generator of Algebraic Structure
- Definition:Generator of Algebraic Substructure
- Definition:Generator of Cyclic Group
- Definition:Generator of Ideal of Ring
- Definition:Generator of Module
- Definition:Generator of Ring
- Definition:Generator of Division Ring
- Definition:Generator of Field
- Definition:Generator of Field Extension
- Definition:Generator of Algebra over Ring
- Definition:Generator of Algebra
- Definition:Generator of Vector Space
- Definition:Infinitesimal Generator of One-Parameter Group

- Geometry:
- Generator, usually referred to on $\mathsf{Pr} \infty \mathsf{fWiki}$ as a generatrix:

## Notation

As well as the notation:

- $\gen {X \cup Y}$

to denote the object generated by $X \cup Y$, it is also possible to use:

- $\gen {X, Y}$

## Also known as

Some sources refer to a **generator for** rather than a **generator of**.

The two terms mean the same.