Is every countable Dedekind domain the ring of integers of some number field? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T14:05:12Z http://mathoverflow.net/feeds/question/106400 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/106400/is-every-countable-dedekind-domain-the-ring-of-integers-of-some-number-field Is every countable Dedekind domain the ring of integers of some number field? LeBlanc 2012-09-05T05:25:43Z 2012-11-01T21:39:29Z <p>Is every countable Dedekind domain the ring of integers of some number field? I tried googling different keywords, but did not find anything. Does anyone know of research in this area?</p> http://mathoverflow.net/questions/106400/is-every-countable-dedekind-domain-the-ring-of-integers-of-some-number-field/106401#106401 Answer by Will Sawin for Is every countable Dedekind domain the ring of integers of some number field? Will Sawin 2012-09-05T05:28:29Z 2012-11-01T20:23:03Z <p>Nope. $\mathbb F_p[x]$, $\mathbb Q[x]$, and all other affine algebraic curves over countable fields, are countable Dedekind domains. None are the ring of integers of a number field.</p>