# 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 Magma
- Definition:Generator of Semigroup
- Definition:Generator of Monoid
- Definition:Generator of Group
- Definition:Generator of Subgroup
- 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:Infinitesimal Generator of One-Parameter Group

## Also known as

Some sources refer to a **generator for** rather than **generator of**. The two terms mean the same.

## Notation

We can also write $\gen {X \cup Y}$ as $\gen {X, Y}$.