5

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.

1 Answers1

3

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

Community
  • 1
Mariano Suárez-Álvarez
  • 135,076
  • 1
    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! – Mariano Suárez-Álvarez Feb 19 '11 at 18:13