Am Freitag 19 Februar 2010 10:42:59 schrieb Hans Aberg:
On 19 Feb 2010, at 00:55, Daniel Fischer wrote:
I'd always assumed "ring" was generalised from Z[n].
As in "cyclic group", arrange the numbers in a ring like on a clockface? Maybe. As far as I know, the term "ring" (in the mathematical sense) first appears in chapter 9 - Die Zahlringe des Körpers - of Hilbert's "Die Theorie der algebraischen Zahlkörper". Unfortunately, Hilbert gives no hint why he chose that name (Dedekind, who coined the term "Körper", called these structures "Ordnung" [order]).
The Wikipedia article "Ring" says he used it for a specific one where the elements somehow cycled back.
Hans
Yes. And I deem a) the english wikipedia a more reliable source of information [concerning things mathematical] than the german, b) Harvey Cohn more trustworthy than either wikipedia. But a quick look at Hilbert's paper didn't reveal the property Cohn mentioned (according to wp) and no explanation of Hilbert why he chose the term. So I remain in doubt. Cheers, Daniel