# unique factorization ring

## English[edit]

### Noun[edit]

**unique factorization ring** (*plural* **unique factorization rings**)

- (algebra, ring theory) 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.