Definition:Generated Submonoid/Generator

Definition

Let $\struct {M, \circ}$ be a monoid

Let $S \subseteq M$.

Let $\struct {H, \circ}$ be the submonoid of $\struct {M, \circ}$ generated by $S$.

Then $S$ is known as a generator of $\struct {H, \circ}$.

Also known as

A generator of a submonoid $\struct {H, \circ}$ can also be referred to as a system of generators of $\struct {H, \circ}$.

Also see

• Definition:Generator of Subgroup

Sources

• 1999: J.C. Rosales and P.A. García-Sánchez: Finitely Generated Commutative Monoids ... (previous) ... (next): Chapter $1$: Basic Definitions and Results