# Examples of polynomial rings $A[x]$ with relatively large Krull dimension

If $A$ is a commutative ring we have the estimate $$\dim (A)+1 \le \dim (A[x])\le 2\dim (A)+1$$ for the Krull dimension, with $\dim (A)+1 = \dim (A[x])$ for Noetherian rings. I am looking for nice examples of rings $A$ so that $A[x]$ has Krull dimension $\dim (A)+2, \dim(A)+3,\ldots ,2\dim(A)+1$.

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