Definition:Submonoid

Definition
A submonoid of a monoid $\struct {S, \circ}$ is a monoid $\struct {T, \circ}$ such that $T \subseteq S$.

We write $\struct {T, \circ} \subseteq \struct {S, \circ}$.

Also see

 * Definition:Subgroup

Generalizations

 * Definition:Subsemigroup

Stronger properties

 * Definition:Unitary Submonoid