unique-factorization domain

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unique-factorization domain [yü¦nēk ‚fak·tə·rə′zā·shə dō‚mān]

(mathematics)

An integral domain in which every element that is neither a unit nor a prime has an expression as the product of a finite number of primes, and this expression is unique except for unit factors and the order of factors. Also known as factorial ring; unique-factorization ring.

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