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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).

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I have learned that it's called "katenär" in german. –  Hanno Becker Apr 22 '10 at 8:40
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 '10 at 8:51
@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! –  user717 Apr 22 '10 at 19:42

2 Answers 2

up vote 12 down vote accepted

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

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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 '10 at 9:23
Thanks a lot! This is a nice term. –  Marc Nieper-Wißkirchen Apr 22 '10 at 9:45

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

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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 '10 at 8:33
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 '10 at 17:57

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