MHB Prove $R\ncong R\left[x\right]$ for Noetherian Ring

[chuyenvien94]

Let $R$ be a commutative Noetherian ring with identity. Prove that $R\ncong R\left[x\right]$ and give an example that the result is not true if $R$ is not Noetherian.

 

[MarkFL]

Can you show what you have tried so our helpers know where you are stuck and/or what mistake(s) you may be making?