Given a field $\mathbb{K}$ which is algebraically closed and of characteristic 0, we can say exactly what the maximal ideals of $\mathbb{K}[x_1,\dots,x_n]$ are and they correspond to points in $\mathbb{K}^n$ (thanks to the Nullstellensatz).
Can I say anything about the maximal ideals of $\mathbb{K}$ if char$\mathbb{K}\neq0$ or if it is not algebraically closed?
Thanks.