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