Square-free element


In mathematics, a square-free element is an element r of a unique [factorization domain] R that is not divisible by a non-trivial square. This means that every s such that is a unit of R.

Alternate characterizations

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.

Examples

Common examples of square-free elements include square-free integers and square-free polynomials.