Revision as of 01:31, 12 August 2008 view source Chobot (talk \| contribs) Bots 167,755 edits m robot Adding: ko:유일분해정역 ← Previous edit		Revision as of 21:45, 24 August 2008 view source Nbarth (talk \| contribs) Autopatrolled, Extended confirmed users, Pending changes reviewers, Rollbackers 35,278 edits →Equivalent conditions for a ring to be a UFD: Ideal class group Next edit →
Line 65: * There is a nice [[two-sided ideal\|ideal]]-theoretic characterization of UFDs, due to [[Kaplansky]]. If R is an [[integral ___domain]], then R is a UFD if and only if every nonzero [[prime ideal]] of R has a nonzero [[prime element]]. * A [[Dedekind ___domain]] is a UFD if and only if its [[ideal class group]] vanishes. In this case it is in fact a [[principal ideal ___domain]]. [[Category:Abstract algebra]]

Unique factorization ___domain: Difference between revisions