Let $k$ be a field of characteristic zero, $x,y$ commuting variables over $k$.

Question 1:Is it possible to characterize all ideals of $k[y,y^{-1}]$ and of $k[x,y,y^{-1}]$?

I guess that the answer to $k[y,y^{-1}]$ is simpler than the answer to $k[x,y,y^{-1}]$?

Question 2:Is it possible to characterize allmaximalideals of $k[y,y^{-1}]$ and of $k[x,y,y^{-1}]$?

**Example:** (1) $I= \langle \frac{x}{y},x \rangle= \langle x \rangle$ is maximal in $k[x,y,y^{-1}]$?

(2) $J= \langle x,y \rangle$ is not maximal in $k[x,y,y^{-1}]$, since $1=y^{-1}y \in \langle x,y \rangle$, so $J=k[x,y,y^{-1}]$.

Thank you very much!