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.

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unique factorization ring
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