A submonoid of a monoid is a subset closed under the monoid operation and containing the same
identity element. For example, consider the monoid formed by the integers
0 through 10 under the operation 
. Then restricting 
and 
from these integers to the set
of elements 
forms a submonoid of the monoid 
under the operation
.
Submonoid
See also
Monoid, Numerical SemigroupExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Submonoid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Submonoid.html