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A principal Ideal domain is an integral domain D in which every ideal in D can be generated by an element in D.

The polynomial in x of integer coefficient $\mathbb{Z}\left [ x \right ]$ is an integral domain. But why is it not a principal ideal domain?

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  • $\begingroup$ You should make a better searching before asking questions, specially if these are very common. $\endgroup$ – Xam Jul 31 '17 at 17:31
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Hint: Is the ideal $(2,x)$ principal?

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