## Krull dimension of Laurent series rings

Let $R$ be a Noetherian commutative ring and let $\dim(R)$ denote the Krull dimension of $R$. For the polynomial ring $R[x]$, we have $\dim(R[x]) = 1 + \dim(R)$. In fact, the same is true if we replace the polynomial ring by the power series ring: again $\dim(R[[x]]) = 1 + \dim(R)$. The situation is a […]