Definition:Strictly Inductive Semigroup/Definition 3

Definition
Let $\struct {S, \circ}$ be a semigroup. Let $\struct {S, \circ}$ be such that either:
 * $\struct {S, \circ}$ is isomorphic to $\struct {\N_{>0}, +}$

or:
 * there exist $m, n \in \N_{>0}$ such that $\struct {S, \circ}$ is isomorphic to $\struct {\map {D^*} {m, n}, +^*_{m, n} }$

where $\struct {\map {D^*} {m, n}, +^*_{m, n} }$ is the restricted dipper semigroup on $\tuple {m, n}$.

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

Also see

 * Equivalence of Definitions of Strictly Inductive Semigroup