Talk:Field of fractions

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The universal property doesn't seem right. I see no reason why the domain itself doesn't satisfy the requirements for Quot(R). Perhaps g should be a field monomorphism? --MarSch 28 June 2005 17:12 (UTC)

[edit] Fraction field, etc.

I do not know why the term "frield of fractions" was changed to "fraction field". I have certainly seen the former, I do not recall seeing the latter. As for comments like "some mathematicians prefer", etc., they might be better placed as notes on usage or perhaps elsewhere, but they seemed out of place in the middle of the discussion.

[edit] Page move?

I agree with those "partisans" - "quotient field" is a desperately confusing term! Would it not be preferable to move the page to one of the other two terms?

  • "Quotient field" - 37,700 Google hits
  • "Field of fractions" - 33,700 Google hits
  • "Fraction field" - 27,100 Google hits
  • "Field of quotients" - 10,800 Google hits (updated to add)

What do those who prefer the term "quotient field" use to refer to the "ring of fractions" where the underlying ring is not an integral domain? — ciphergoth 16:04, 23 February 2006 (UTC)

Well, since you ask... I suspect "quotient field" came about from talking about the "field of quotients", though the term seems to be even more rare acccording to google. Personally, I would prefer "field of fractions" or "field of quotients", but if it is not the most common term then there is little to be done about it other than put redirects from "field of fractions" and mention it in the text. The term is common and used, so whether or not it is confusing is somewhat besides the point. There is plenty of mathematical terminology that is confusing, both desperately and mildly so. I do not think there is a warrant to move from the (apparently, judging from your quick google survey) most common term to another term simply because we do not like the former or prefer the latter. While the text, speaking of "partisans" and the like, seems overly judgemental, other than redirects and perhaps a bit of cleaning up on this text I do not think a page move is warranted. Magidin 02:05, 26 February 2006 (UTC)
You make a good case, but let me have a go at bringing you around...
Where there is more than one term for something, Wikipedia tries to use one term consistently, and this is in itself exercising a little bit of wiggle room to teach an inconsistently-taught subject consistently. Wikipedia should certainly not make its own terms up or make idiosyncratic choices, but I think the difference in popularity is sufficiently small that we may allow other considerations to weigh in on what term Wikipedia should settle on, and which term is least confusing is a good consideration.
My Google survey shows that "quotient field" is used less than 35% of the time, and "field of fractions" less than 31% of the time; that's not a big difference. Also, "field of fractions" and "fraction field" are obvious variants of each other, so there's a case to be made that "quotient field" is the idiosyncratic choice.
Finally, we still need a term for "ring of fractions"... — ciphergoth 09:06, 26 February 2006 (UTC) (updated percentages to take "field of quotients into account — ciphergoth 11:57, 26 February 2006 (UTC))
One other point - how many of those Google hits for "quotient field" is Wikipedia responsible for? — ciphergoth 09:12, 26 February 2006 (UTC)
I think of this as the field of fractions, and 'quotient field' is unpleasantly ambiguous. Charles Matthews 10:01, 26 February 2006 (UTC)
I agree: when I hear "quotient field", I always check twice whether they're talking about the field of fractions, or about the quotient of a commutative ring by a maximal ideal, giving a field. I suspect that some of the Google hits for "quotient field" reported above refer to the second notion. AxelBoldt 17:08, 26 February 2006 (UTC)
OK, that's good enough for me - two of the three major participants like it, and the only argument against is a 4% difference in Google popularity, which may be misleadingly large for two reasons. In addition many Wikipedia pages already point to "field of fractions" and get redirected. I'll make the move. — ciphergoth 18:02, 26 February 2006 (UTC)