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I am looking for the correct technical term in German for the notion of catenary ring in commutative algebra.

Does anyone know?

For those who don't know what a catenary ring is but would like to: A Noetherian commutative ring A is called catenary if the following codimension formula holds for irreducible closed subsets T ⊆ Y ⊆ Z of Spec A:

codim(T, Z) = codim(T, Y) + codim (Y, Z).

edited Apr 22 2010 at 10:32

Joel David Hamkins
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asked Apr 22 2010 at 7:58

Marc Nieper-Wißkirchen
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I have learned that it's called "katenär" in german. – Hanno Becker Apr 22 2010 at 8:40

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Do you know whether this is the correct technical term (as it looks like a made-up word one will not find in a German dictionary) or whether it is just being used by someone who also does not know how to translate "catenary" properly? – Marc Nieper-Wißkirchen Apr 22 2010 at 8:51

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@Hanno: Wow, entering "katenär" in google gives 16 hits (already including your answer :)). I have never heard/seen this word; but on the one hand I never talked about these rings in German and on the other hand google books gives at least 3 relevant hits, so it seems that some mathematicians indeed use it! – S1 Apr 22 2010 at 19:42

K Halb · Accepted Answer · 2010-04-22 09:04:28Z UTC

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It should be "Kettenring", see for example p. 148 in Brodmann, Algebraische Geometrie.

answered Apr 22 2010 at 9:04

K Halb
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This makes sense because "catenary" is just the Latin-derived English word for "chain", so German should use its own word for "chain". – John Stillwell Apr 22 2010 at 9:23

Thanks a lot! This is a nice term. – Marc Nieper-Wißkirchen Apr 22 2010 at 9:45

Christian Perfect · Answer 2 · 2010-04-22 08:11:46Z UTC

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according to this German Maths Dictionary, it's 'kettenlinie'

answered Apr 22 2010 at 8:11

Christian Perfect
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This doesn't make sense. In English, "catenary" can also stand for a curve given by the graph of the cosh function, so it can be used as a noun (in this case) or as an adjective (in the case of catenary rings). In German, "Kettenlinie" is just a noun, so it cannot stand in front of the word "ring". Furthermore, the meaning of "Kettenlinie" is exactly the meaning of the English catenary when it stands for the curve; and the meaning of "Kettenlinie" doesn't have anything to do with chains of prime ideals. – Marc Nieper-Wißkirchen Apr 22 2010 at 8:33

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Don't you think it a little unfair downvoting the answer? The original question title was "What is the German translation of "catenary"" - it was then changed to "catenary ring". – vonjd Apr 22 2010 at 17:57

vonjd · Answer 3 · 2010-04-22 08:30:35Z UTC

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Katenoide, also Seilkurve, Kettenlinie or Kettenkurve

http://de.wikipedia.org/wiki/Katenoide

answered Apr 22 2010 at 8:30

vonjd
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Please see my comment above. – Marc Nieper-Wißkirchen Apr 22 2010 at 8:35

Don't you think it a little unfair downvoting the answer? The original question title was "What is the German translation of "catenary"" - it was then changed to "catenary ring". – vonjd Apr 22 2010 at 17:57

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I voted it down and I think it's not unfair because it's completely wrong. :) But I didn't know about the first version of the title! – S1 Apr 22 2010 at 19:33

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Even with the first version of the title, it should have been clear by reading the question that the question was about catenary rings and not about the catenary. [ If the question was about the German translation of the catenary, the best answer would probably have been to vote my question down as the English Wikipedia article of the catenary already gives the link to the German translation. :-) ] – Marc Nieper-Wißkirchen Apr 23 2010 at 6:32

You are right, I can accept that... Anyway: It always hurts to get downvoted but I understand this time I had it coming :-( – vonjd Apr 23 2010 at 9:25

What is the German translation of “catenary ring”?

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