On 19 Feb 2010, at 12:12, Daniel Fischer wrote:
...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.
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.
The term "group" was introduced Évariste Galois, though he meant what we call a cancellative monoid, but since they are finite, have inverses. So perhaps Hilbert made play on that word: a group is a small number of people, a ring larger, like a gang. Hans