I propose that this is probably better to use official names from Math:
The five-lemma cannot be generalized to arbitrary Artin ring.
Artin was a German-Turkish woman.
http://scholar.google.no/schola...n&as_sdt=0%2C5
This sentence is quite old, but when you try to find something like this, over Google you got only Danish version, so those forms we now have probably originate from Danish.
artinian -> Artinian
The sentence cannot be modified due to the presence of audio, even if the audio is disabled. I see instances of uncapitalized "artinian" on the web anyway, so I'm going to remove the "@change" tag.