Talk:Euclidean domain/Archive 1

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Archive 1

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Latest comment: 15 years ago5 comments5 people in discussion

I felt that the information provided by 128.40.56.75 was worth keeping, if it's correct. Yes, it was poorly formatted, so I've made a first stab at doing better. I've tried to format the references consistently, and I hope I haven't changed them semantically. I have not verified that the actual information provided by 128.40.56.75 is correct, but it sounds very reasonable, so I have no reason to doubt it. Adam1729 03:27, 19 February 2007 (UTC)

I feel like the inequality should stay in the defintion. This inequality isn't obvious for the gaussian integers for example. stephane — Preceding unsigned comment added by 24.16.72.51 (talk) 10:53, 12 August 2007 (UTC)

The paper "Kenneth Rogers: The Axioms for Euclidean Domains" in AMM [1] compares various definitions of Euclidean domains -- N(a)<=N(a)N(b); N(ab)=N(a)N(b) and "the range of N is subset of Z, bounded from bellow". This could be added as a reference since it is related to the stuff in the article. (Perhaps also the text could be reformulated using this article, if no better source is found.) --Kompik (talk) 12:25, 20 March 2008 (UTC)

Could someone else please check me on this one - It looks like the inclusions at the top of the article are running the wrong way. The integers form a PID, for example, but they certainly don't contain the field of rationals, which is what the chain seems to imply.Ike Benjamin (talk) 16:19, 21 September 2008 (UTC)

Hello Ike Benjamin, the inclusions are correct. In your example, what they indicate is that the class of PIDs contains the class of fields, that is, every field is PID - they do not mean that every PID contains a field or so. Ninte (talk) 09:47, 6 February 2009 (UTC)