Category:Definitions/Subsemigroups

This category contains definitions related to Subsemigroups.
Related results can be found in Category:Subsemigroups.

Let $\struct {S, \circ}$ be an algebraic structure.

Let $T \subseteq S$ such that $\struct {T, \circ {\restriction_T} }$, where $\circ {\restriction_T}$ is the restriction of $\circ$ to $T$, is a semigroup.

Then $\struct {T, \circ {\restriction_T} }$ is a subsemigroup of $S$.