Unique factorization ___domain: Difference between revisions

Revision as of 08:24, 27 November 2007

Revision as of 18:43, 27 November 2007

Line 55:

Under some circumstances, it is possible to give equivalent conditions for a ring to be a UFD.

* A [[Noetherian]] integral ___domain is a UFD [[if and only if]] every [[height (ring theory)|height]] 1 [[prime ideal]] is principal.

* An integral ___domain is a UFD if and only if the ascending chain condition holds for principal ideals, and any two elements of ''A'' have a least common multiple.