Exercise 111.64.6 (Two vectors). Let $A = \mathbf{Z}[a_1, a_2, a_3, b_1, b_2, b3]$. Set $a = (a_1, a_2, a_3)$ and $b = (b_1, b_2, b_3)$ in $A^{\oplus 3}$. Consider the set

Prove the $Z$ is a closed subset of $\mathop{\mathrm{Spec}}(A)$.

What is the dimension $\dim (Z)$ of $Z$?

What would happen to $\dim (Z)$ if we replaced $\mathbf{Z}$ by a field?

## Comments (0)