SQUARE-FREE

In mathematics, an element ''r'' of a unique factorization domain ''R'' is called 'square-free', if it is not divisible by a non-trivial square. That is, if every ''s'' such that $s^2mid\; r$ is a unit of ''R''.
Square-free elements may be also characterized using their prime decomposition. The unique factorization property means that a non-zero non-unit ''r'' can be represented as a product of prime elements
:$r=p\_1p\_2cdots\; p\_n$
Then ''r'' is square-free if and only if the primes ''p_i'' are pairwise non-associated (i.e. that it doesn't have two of the same prime as factors, which would make it divisible by a square number).
Common examples of square-free elements include square-free integers and square-free polynomials.