Can I compute the Krull dimension of $\mathbb{Q} + x \mathbb{R}[x]$ knowing elementary facts only? (This question comes from Atiyah-MacDonald)
I know that $\dim (\mathbb{Q}[x]) = 1$ and $\dim (\mathbb{R}[x]) = 1$. Can I compute $\dim (\mathbb{Q} + x \mathbb{R}[x])$ from these two facts?
Can I compute $\dim (\mathbb{Q} + x \mathbb{R}[x])$ knowing elementary facts (Atiyah-Macdonald level)?