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Let $R$ be a commutative ring with unit. Let $R_p$ be a domain for all $p\in SpecR$ and let $SpecR$ be connected. Is it true that $R$ is a domain or can someone provide a counterexample. Note here that $R$ is not necessarily a Noetherian ring. For a Noetherian ring this is easy.

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See https://mathoverflow.net/questions/7477/non-integral-scheme-having-integral-local-rings

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    To provide this answer, I had to solve a captcha. Presumably, after all the time spent in the site, my posting a link is a clear sign of me beginning to be a spammer. *Great algorithm, guys!*2011-02-19