Am Freitag 19 Februar 2010 00:24:23 schrieb Richard O'Keefe:
On Feb 19, 2010, at 3:55 AM, Daniel Fischer wrote:
Am Donnerstag 18 Februar 2010 14:48:08 schrieb Nick Rudnick:
even in Germany, where the term «ring» seems to originate from, since at least a century nowbody has the least idea it once had an alternative meaning «gang,band,group»,
Wrong. The term "Ring" is still in use with that meaning in composites like Schmugglerring, Autoschieberring, ...
The mathematical ring is OED ring n1 sense 12. The group of people sense is sense 11, immediately above it. "Drug ring" is still in use. 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]).