Definition:Generated Submonoid/Generator
< Definition:Generated Submonoid(Redirected from Definition:Generator of Submonoid)
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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
Sources
- 1999: J.C. Rosales and P.A. García-Sánchez: Finitely Generated Commutative Monoids ... (previous) ... (next): Chapter $1$: Basic Definitions and Results