Given a definition of $R=2\Bbb Z$ prove that ring $R[x]$ is not noether.
I assume that the proof should be based on the fact that a ring is noether if and only if any ideal is finitely generated. However, I'm struggling with constructing a non-finitely generated ideal, because only ideals I can think of are "root-based" (i.e. polynomials that have certain roots), that are, of cource, finitely generated.
I would be very grateful for a description of such ideal or a piece of work that can explain the structure of polynomial ring ideals in detail.