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?
Find all ideals of $\mathbb Q$
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abstract-algebra
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3We can't say _the_ ideal since $\{0\}$ is also an ideal. – 2012-02-01
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12Hint: $\mathbb{Q}$ is a field. – 2012-02-01
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0A much more interesting question is: What are the subrings of $\mathbb Q$? – 2012-02-01
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2See 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