# I want an example of principal ideal domain that is not a Jacobson ring (PID but non-Jacobson ring) [closed]

Please give me an example principal ideal domain that is not a Jacobson ring. Its better this ring be commutative.

## closed as off-topic by user26857, C. Falcon, Shailesh, JonMark Perry, Claude LeiboviciMay 3 '17 at 8:40

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• You have to look for a principial ideal domain with vanishing jacobson radical. – user302982 Jan 9 '16 at 9:16
• I meant non vanishing. Look here en.wikipedia.org/wiki/Jacobson_ring – user302982 Jan 9 '16 at 9:22
• It hasn't example for my question. i saw it. – ruholla kh Jan 9 '16 at 11:52

Simply $\Bbb Z_{(2)}$ works: the localization of the integers at the complement of the prime ideal $2\Bbb Z$.