Definition:Generator


 * 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 Algebraic Substructure
 * Definition:Generator of Subsemigroup
 * Definition:Generator of Submonoid
 * 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


 * Category Theory:
 * Definition:Generator of Category


 * Geometry:
 * Definition:Generator of Cone
 * Definition:Generator of Cylinder

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 $\gen {X, Y}$.

Also see

 * Definition:Generated