# An integral domain that is not a principal ideal domain [duplicate]

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?

• You should make a better searching before asking questions, specially if these are very common. – Xam Jul 31 '17 at 17:31

Hint: Is the ideal $(2,x)$ principal?