Definition:Subsemigroup

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

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