WikiProject Mathematics (Rated Start-class, Mid-importance)
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Field: Number theory

I don't understand the definition. What is the topology on adeles to make it a locally compact group? AFAICS the usual product topology is not locally compact in this case. EJ 14:51, 20 Aug 2004 (UTC)

Correct. But the restricted product topology is. The adeles as a whole are the union of more 'reasonable' subsets looking like product of p-adic integers over almost all p (compact), cartesian product with a finite product of p-adic numbers and the real numbers (locally compact). Every given adele is in such a 'reasonable' set.

Charles Matthews 16:24, 20 Aug 2004 (UTC)

Thanks for a reply. Notice that the restricted product page doesn't describe the topology either, which is why I asked in the first place. Just to make sure I understand you correctly: the res. prod. topology coincides with prod. topology on each 'reasonable' subset, thus a subset of the restricted product is open iff it is relatively open in each 'reasonable' subset; in other words, the res. prod. topology is inductively generated by prod. topologies on 'reasonable' subset. Is this correct?
EJ 11:16, 21 Aug 2004 (UTC)

Yes, that sounds right. Thanks for pointing out the deficiency of the RP page - should be fixed up. Charles Matthews 11:47, 21 Aug 2004 (UTC)

## Idèle vs idele

I have reverted this change which changes idèle to idele throughout, and adds the alternative adèle, with an edit summary that fails to mention those changes. This is the sort of change that tends to produce strong reactions, and so should be discussed here per WP:BRD. For what it's worth, Neukirch (1999) uses the form idèle and adèle. Deltahedron (talk) 18:10, 17 April 2013 (UTC)

It was not an arbitrary change. You can see that there was no standard before my edit. I just standardized the spelling that has already been established both on Wikipedia (see also Adelic algebraic group) and in the mathematical literature (confer 1; 2, 3). Neukirch (1999) is obviously not the only English-language source on the subject. --Omnipaedista (talk) 02:03, 18 April 2013 (UTC)
It was a change made without discussion here and without a suitable edit summary. If the spelling has been standardised here on Wikipedia, please link to the discussion where that consensus was established. The spelling has clearly not been standardised in the mathematical literature, and if you think it has please cite an authoritative source. Google book searches do not constitute an authoritative source. Deltahedron (talk) 06:29, 18 April 2013 (UTC)
I should have indeed provided a suitable edit summary. As far as Wikipedia is concerned the "no accent" form has been "established" pragmatically. The original version of 'Adele ring' and the long-standing versions of the articles 'Adelic algebraic group', 'Idele class character' feature no accent. The addition of an accent here was made by a single user who him/herself was not even consistent about it. As far the mathematical literature is concerned I deem that there is no authoritative source available establishing a priori which is the standard, so we could for the moment rely on Google Book searches and ArXiv searches. In any case even if the Wikipedia community eventually chooses for some reason to employ the accented form of the word 'idele', it would be wise to do so consistently throughout Wikipedia, and also to employ the accented form of the word 'adele' to avoid confusion. --Omnipaedista (talk) 11:23, 18 April 2013 (UTC)

## Source of the term "adele"

Oscar Goldman claimed to be the originator of the contraction. He was taking notes for a series of lectures by Chevalley, who referred to them as "additive ideles" at the time. According to Goldman, when Chevalley noticed the contraction Goldman was using, he liked it and adopted it. Goldman always insisted on the pronunciation "add-ell." — Preceding unsigned comment added by 108.28.113.226 (talk) 19:05, 31 May 2013 (UTC)

This comment would be very much more valuable if you could provide a source for it. Colin McLarty (talk) 04:12, 9 June 2013 (UTC)

I personally heard Goldman's pronunciation of "add-ell." The story about taking notes from Chevalley is a personal communication from Goldman's student Robert Rubin. — Preceding unsigned comment added by 108.28.113.226 (talk) 14:27, 12 June 2013 (UTC)