Posts Tagged ‘math.RA’

An etymological question

December 18, 2009

Galois was of course the first to highly successfully use the notion of a field. However, if ones reads his papers they’ll see that he never explicity gave the concept of an algebraic structure closed under addition, subtraction, commutative multiplication, and division a name. Dedekind would be the first to do that; he gave the name Körper, or “body,” to what we’d today call a number field. A couple of decades later, E.H. Moore of Chicago would introduce the term “field” in English.

“Körper” caught on fairly quickly among Continental mathematicians, giving us the French corps, and from there it spread to Spanish and Portuguese; in the other direction, the German mutated into Hungarian “test” and Polish “ciało”, both essentially with the same meaning of “body.”

However, in Italian and most of the Slavic languages, the word for “field” is also the agricultural term. This means that the algebraic terminology didn’t solidify until considerably later, probably between the World Wars at earliest. This is understandable; while both Italy and Russia had strong mathematical communities around the turn of the last century, they were somewhat isolated and if nothing else had relatively fewer top-tier algebraists than the French or, especially, the German schools.

What’s really curious is the following: In both Italian and Russian, as I mentioned, the word for English “field” is a literal translation of “field.” In pretty much every language, the word for “ring” can also refer to a thing that you wear on your finger. But in Italian and (several of) the Slavic languages — and in these languages alone, as far as I know — the word for “skew field”, or “division ring”, translates to English as “body”! This seems to me to be a rather exceptional situation — surely either a modification of “ring” or of “field” will do, as in every other language, but it seems not to be the case. So there are two open problems here:

  1. Explain the situation that caused “field” to replace “body” to refer to a commutative division ring, but not to refer to a division ring in general, in Italian and Russian.
  2. Are there any other examples of crufty terminology that’s unique to one or two languages (or closely-related language families?)
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