Let $R$ be a Noetherian ring and consider $S=R[x,x^{-1}]$. I would like to show that $\mathrm{dim}(S)=\mathrm{dim}(R)+1$.
I know that for a Noetherian ring $A$, $\mathrm{dim}(A[t])=\mathrm{dim}(A)+1$, but I have trouble seeing how I can make use of this information to prove the above result.
Any hint/help will be very useful. Thanks in advance.