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Let $\mathbb Q$ be the set of all rational numbers. I would like to know what the ideal for $\mathbb Q$ as ring is. I think the ideal of $\mathbb Q$ is $\mathbb Q$, Am I right?

  • 3
    We can't say _the_ ideal since $\{0\}$ is also an ideal.2012-02-01
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    Hint: $\mathbb{Q}$ is a field.2012-02-01
  • 0
    A much more interesting question is: What are the subrings of $\mathbb Q$?2012-02-01
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    See also this question: [A ring is a field iff the only ideals are (0) and (1)](http://math.stackexchange.com/questions/101157/a-ring-is-a-field-iff-the-only-ideals-are-0-and-1)2012-02-01

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