Is there any characterization for a commutative ring to be a quotient of a Dedekind domain?
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3$\begingroup$ Let $R$ be a dedekind domain and $I$ and ideal, and let $\prod \mathfrak{p}_i^{e_i}$ be $I$'s factorization. Then $R/I = \prod R/\mathfrak{p}_i^{e_i}$ by the CRT, and each $R/\mathfrak{p}_i^{e_i}$ is an artin ring. So $R/I$ is a finite direct product of artin rings. The question is which such finite products can occur. $\endgroup$– benblumsmithCommented Jul 11, 2016 at 16:21
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$\begingroup$ Make that local artin rings. $\endgroup$– benblumsmithCommented Jul 11, 2016 at 16:40
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$\begingroup$ Another major condition is that the Zariski tangent space of each $R/\mathfrak{p}_i^{e_i}$ is one dimensional. We also get a restriction on the residue fields from mathoverflow.net/questions/176117/… . $\endgroup$– David E SpeyerCommented Jul 11, 2016 at 17:34
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1$\begingroup$ above should say "one or zero" dimensional. $\endgroup$– David E SpeyerCommented Jul 11, 2016 at 18:46
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