Talk:Local ring

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About the noetherian condition - can I explain that Zariski in particular took local ring to be noetherian? This is however not the modern convention. It needs to be mentioned here, therefore. Making the convention Wikipedia-wide is a practice followed, for example, in defining a ring (mathematics) always to be unital here. It is therefore appropriate to explain here that the convention is expected everywhere on WP.

Charles Matthews 09:55, 4 May 2004 (UTC)[reply]

Be careful using rollback because (a) it gives me no idea what your objection is since there's no edit summary and you wrote nothing in Talk, (b) it removes all my edits, such as here my grammar fix is -> are, which makes it look like you have other motives, and (c) it runs the risk of aggravating people. Anyway, as for the issue, I've seen discussed several places the problems with referring to Wikipedia explicitly like that, one being that this is supposed to be a GPL'd encyclopedia which can be forked, recopied elsewhere, and so on, and so should not use this sort of self-reference. You are correct that there is precedent for doing so, but that doesn't mean it's a good idea. Perhaps using an indexical such as "this encyclopedia" would serve, as that would cover all the related articles? (Hm, there's no indexical article, how sad.) -- VV 20:24, 4 May 2004 (UTC)[reply]

I had in fact overlooked the is/are edit you made. You are correct that it would have been better for me to deal with this by hand, looking at that alone.

On the substantive point, though, I cannot agree with you. It's not really a tenable one, in this case. Local ring was once assumed to include an extra noetherian hypothesis. This point must be mentioned here, to retain NPOV. But this one page should deal with that point. It is not tolerable to bring it up every time local ring is used. Anyone in the field would be aware of this point; and it saves time to announce a convention here.

Charles Matthews 20:52, 4 May 2004 (UTC)[reply]

This is not an issue of whether there should be an encyclopedia-wide convention but rather how to note it. That's the point of my proposed indexical. -- VV 21:00, 4 May 2004 (UTC)[reply]

If I knew what an indexical was, I'd be in a better position to understand the comment ...

Charles Matthews 21:07, 4 May 2004 (UTC)[reply]

I thought my example made that clear: something like "this encyclopedia". (An indexical is a word such as here, this, me, which is relative to the speaker/listener/context.) -- VV 21:13, 4 May 2004 (UTC)[reply]

"As for any topological ring, one can ask whether (R, m) is complete (as a topological space)" Is there really such a thing as a complete topological space? Completely metrizable, sure, but here we are really talking about a property of the m-adic metric. Perhaps someone should change the word "topological" to "metric"? — Preceding unsigned comment added by 82.7.71.210 (talk) 11:47, 12 February 2012 (UTC)[reply]

More generally, a poset P with a greatest element 1 might be called "local" if the set P\{1} has itself a greatest element. A ring R is local iff the poset of left ideals of R is local iff the poset of right ideals of R is local. GeoffreyT2000 (talk) 19:31, 7 May 2015 (UTC)[reply]