unique-factorization domain

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.