Talk:Euclidean domain/Archive 1

Comments
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 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)

Changes Needed
This article lacks many links to other articles, for example what does $$\inf_{x \in R \setminus \{0\}}$$ mean? I know that it's the infimum, but would a casual reader? If the article isn't meant for casual readers - which of course it is - then the slow and informal introduction is not needed.

There is also a clash of notation. The symbol $$\mathbb{Z}$$ is used for the integers at the start of the article, but Z is used later. Again, the notation $$\mathbb{Z}^{\ge 0}$$ must be explained for the benefit of the casual reader.

Δεκλαν Δαφισ  (talk)  17:51, 18 June 2009 (UTC)