[Haskell-cafe] Category Theory woes

Hans Aberg haberg at math.su.se
Fri Feb 19 06:53:56 EST 2010

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.


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