- Square-free
In

mathematics , an element "r" of aunique factorization domain "R" is called**square-free**if it is not divisible by a non-trivial square. That is, 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 element s:$r=p\_1p\_2cdots\; p\_n$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 integer s andsquare-free polynomial s.

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