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Aug 15, 2012 at 22:53 comment added user9072 Just regarding the point 'abstract number ring' this merely means that the quotient by any ideal is finite (and some nondegeneracy condition, not a field and infinite). Pete Clark seems to lieke them math.uga.edu/~pete/aant.pdf
Aug 15, 2012 at 21:57 comment added user16974 @lemniscate: I got the point, which answers my question in the negative.
Aug 15, 2012 at 21:39 comment added Alexander Gruber Is it true that the $I_k$ must be necessarily be all of the distinct ideals of $D$? If so the $n_k$ would have to have appropriate multiplicities for the $\mathbb{Z}_p[x]$ example.
Aug 15, 2012 at 21:37 vote accept CommunityBot
Aug 15, 2012 at 21:21 history answered Andreas Blass CC BY-SA 3.0