Square element

Definition

Suppose $(S,*)$ is a magma, i.e., $S$ is a set and $*$ is a binary operation on $S$. Then, an element $x\in S$ is termed a square element or square if there exists $y\in S$ such that $x=y*y$.

Note that $S$ may be a group or semigroup, which is the typical context of use; however, the notion of square element makes sense even for non-associative binary operations.