I am working on a problem, where it happens that fields, that do not have the property of being algebraically closed, cover the important cases. Now I thought quite a long time about the question of how to call such fields. Should it be "non-algebraically closed fields" or "not algebraically closed fields"?
On the one hand, in general, if we have any adjective $A$, we negate it by non-$A$. For instance, the contrary of a "soft question" should be a "non-soft question". "Not soft question" would be grammatically false. On the other hand "non-algebraically closed" looks unlogical since one could think that the "non" only has to do with the "algebraically" and is independent from the "closed".
But now again if I say "Let $K$ be a not algebraically closed field." this sounds very unnatural to me.
As I am not a native speaker in English, I would be very thankful for any of your help! Thanks in advance!