Square element

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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.