A ring R is a Unique Factorization Domain (UFD) if for every non zero non unit a in R,
1. There exist irreducibles p1,p2,....,pn in R such that a=p1p2...pn, and
2. If there are irreducibles q1,q2,...,qn in R such that a=q1q2...ql then l=n and there exists a one-to-one correspondence between the ps and the qs so that corresponding numbers are associate.