As an example of a substructure, we show that the consecutive performance of the binary operation "$\ast$" on the same element creates a substructure in a monoid.
If $x$ is an element of a monoid $(X,\ast)$, then the subset of all powers $x^n$, $(n=0,1,2,\ldots)$ is a substructure of $X$, called its submonoid.
Proofs: 1
