Definition:Generator

Finitely Generated
The concept of a generator is usually defined in the context of particular types of structure, as follows.

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 $\left\langle {X \cup Y} \right\rangle$ as $\left\langle {X, Y} \right\rangle$.

Also see

 * Definition:Generator of Algebraic Structure
 * Definition:Generator of Magma
 * Definition:Generator of Semigroup
 * Definition:Generator of Monoid
 * Definition:Generator of Group
 * Definition:Generator of Ideal of Ring
 * Definition:Generator of Module
 * Definition:Generator of Field Extension


 * Definition:Generator of Category
 * Definition:Infinitesimal Generator of One-Parameter Group