Editing Prime element (section)

==Irreducible elements==
{{Main|Irreducible element}}
Prime elements should not be confused with [[irreducible element]]s.  In an [[integral domain]], every prime is irreducible<ref>{{harvnb|Hungerford|1980|loc=Theorem III.3.4(iii)}}</ref> but the converse is not true in general.  However, in unique factorization domains,<ref>{{harvnb|Hungerford|1980|loc=Remark after Definition III.3.5}}</ref> or more generally in [[GCD domain]]s, primes and irreducibles are the same.