What is the opposite of unique factorization ring?
We do not currently know of any antonyms for unique factorization ring.
The noun unique factorization ring is defined as:
A ring in which every non-zero, non-unit (i.e., proper) element can be factored into a product of prime elements (not necessarily distinct), such that such factorization is unique up to permutation of the factors and the replacing of primes by their associate primes.