Definition talk:Quotient Field

Should this be $\forall x \in F: \exists z \in D, y \in D^*: x = \dfrac z y$? --Cynic (talk) 23:23, 25 May 2010 (UTC)

Yes indeed. Or something like that. Swapped z and x in the forall/exists instead. --Matt Westwood 05:35, 26 May 2010 (UTC)

I think this is better -- if / when I write a page on universal properties, uniqueness will be automatic. I also thought it was confusing to have every extension of $F$ also being a quotient field of $D$. --Linus44 21:11, 23 February 2011 (CST)

The way I've been constructing pages is to make the definition as bald and simple as possible, i.e. "a" quotient field, then linking with a "see also" to different pages that provide the proofs that they exist and are unique.

We could change to include the existence/uniqueness proof on the same page as the definition, but I'm not sure this is always intrinsically a better approach.

Particularly in this case, where the construction of the quotient field is part and parcel of the fairly complicated inverse completion construction which applies in more than one context.

I'm fairly sure we've already got separate pages proving the existence / uniqueness result here anyway.

But whatever. If others have a different vision as to how this website is to develop, go for it. Just that every time we have a change of direction, we have to go back and change what's already there, and this is slowing down the development of new pages.

Just my 2-cents worth. --prime mover 00:20, 24 February 2011 (CST)

This is true. Its easy enough to change pages retrospectively that it makes sense to do so later if it is necessary, rather than for each user to begin from the beginning.

On the other hand I don't think that having terse definitions is always good, this often doesn't indicate exactly what the definition means.

I'll try not to get bogged down with unnecessary changed to what's already written, but I think that there is no harm in appending a discussion to existing pages. -- Linus44 08:03, 24 February 2011 (CST)

Yer all right. I looked at this again and yeh, nothing wrong with it. IMO pages are better short than long, as it's so easy to feel that everything and the kitchen sink needs to go in (see Definition:Logical Graph for the worst example of a page that does not really fit the style of this website). But now I've taken time to have a good look at this, then yeah, no worries. --prime mover 15:25, 24 February 2011 (CST)

I've been thinking about this, I agree that relatively short pages are probably better. Sometimes there are significantly different ways of expressing a definition, in which case one can be a theorem, otherwise both probably aren't necessary.

I think anyway -- judging by the page histories you seem to have written a large proportion of the site yourself, so I'll defer to you on such matters. --Linus44 21:18, 26 February 2011 (CST)