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, every "s" such that 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:Then "r" is square-free if and only if the primes "pi" 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.
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