A submonoid is a subset of the elements of a monoid that are themselves a monoid under the same monoid operation. For example, consider the monoid formed by the nonnegative integers under the operation . Then restricting and from all the integers to the set of elements forms a submonoid of the monoid under the operation .
Submonoid
See also
MonoidExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Submonoid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Submonoid.html