Talk:Euclidean domain
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| Mathematics rating: | Start Class | Low Priority | Field: Algebra | ||
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[edit] 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
The paper "Kenneth Rogers: The Axioms for Euclidean Domains" in AMM [1] compares various definitions of Euclidean domains -- N(ab)<=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)
