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

• Results about strictly inductive semigroups can be found here.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 16$: The Natural Numbers: Exercise $16.8 \ 2^\circ$