Definition:Strictly Inductive Semigroup/Definition 2

Definition
Let $\struct {S, \circ}$ be a semigroup. Let there exist an epimorphism from $\struct {\N_{>0}, +}$ to $\struct {S, \circ}$.

Then $\struct {S, \circ}$ is a strictly inductive semigroup.

Also see

 * Equivalence of Definitions of Strictly Inductive Semigroup