Definition:Generated Submonoid/Generator

Definition
Let $\struct {M, \circ}$ be a monoid

Let $S \subseteq M$. Let $\struct {H, \circ}$ be the submonoid of $\struct {M, \circ}$ generated by $S$.

Then $S$ is known as a generator of $\struct {H, \circ}$.

Also known as
A generator of a submonoid $\struct {H, \circ}$ can also be referred to as a system of generators of $\struct {H, \circ}$.

Also see

 * Definition:Generator of Subgroup