Talk:Euclid's Lemma for Irreducible Elements

This statement holds in the more general case where $D$ is a unique factorization domain. Should I revise this article and modify the proof for the more general scenario, or should I create a new article to prove the result for UFDs?

--Ixionid 23:55, 2 February 2012 (EST)


 * Write another page, create a master page, transclude all the various results on this subject accordingly, and then reconfigure all the citation links so they relate to the appropriate page. Should only take you a few minutes. :-) --prime mover 01:43, 3 February 2012 (EST)


 * ... but seriously ... the general philosophy is that each result needs to be written as a separate page. If it happens that the proof is substantially the same for the less abstract class of objects, then (for example) the proof for Euclidean Domain would consist of "A Euclidean Domain is a unique factorization domain, so the result [link to it] can be applied" or however it is worded.


 * Note that it is not appropriate to do the same for the set of natural numbers / integers, as that particular result comes from the direction of number theory. Not everyone studying number theory should be expected also to have studied abstract algebra, and so should not be expected to be able to follow arguments based on the properties of unique factorization domains and Euclidean domains. So we do need to keep the proof Euclid's Lemma for Prime Divisors.


 * Once we have all these proofs for various objects, what I would then do is develop a master page which consists of little more than transclusions of these various results, each one of which stands alone as a page in its own right - but not to worry about that, it's something I would probably do when I wasn't in the mood for thinking about something difficult. --prime mover 02:39, 3 February 2012 (EST)