Definition:Submonoid

Definition
A submonoid of a monoid $\left({S, \circ}\right)$ is a monoid $\left({T, \circ}\right)$ such that $T \subseteq S$.

We write $\left({T, \circ}\right) \subseteq \left({S, \circ}\right)$.

Also see

 * Definition:Subgroup

Generalizations

 * Definition:Subsemigroup

Stronger properties

 * Definition:Unitary Submonoid