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Obviously it's not $\mathbb{Z}$.

Infinity
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    See: http://math.stackexchange.com/questions/144022/subideals-of-an-ideal . – Eric Towers Jun 09 '16 at 05:28
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    There's a classic text that's sadly out of print-Rings, Modules and Linear Algebra by B. Hartley, T.O. Hawkes,that contains many wonderful examples and counterexamples in basic ring and module theory.I was trying to get it republished last year and the estate refused. I think it's a perfect reference for this question and those like it. – Mathemagician1234 Jun 09 '16 at 05:47

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