Definition:Subsemigroup

Definition
A subsemigroup $\left({T, \circ}\right)$ of an algebraic structure $\left({S, \circ}\right)$ is a semigroup $\left({T, \circ}\right)$ such that $T \subseteq S$.

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