I am just wondering if that is the case in the ring $\mathbb{Q}[x]$ because in class we showed that it is maximal in $\mathbb{Z}[x]$
I believe that (x,2) is also not principal in $\mathbb{Q}[x]$
I am just wondering if that is the case in the ring $\mathbb{Q}[x]$ because in class we showed that it is maximal in $\mathbb{Z}[x]$
I believe that (x,2) is also not principal in $\mathbb{Q}[x]$
Hint $\ 2$ is a unit (invertible) in $\Bbb Q,$ and any ideal containing a unit $u$ contains $\,u u^{-1}\! = 1$.
Note also that $\Bbb Q[x]$ is a PID, because it is Euclidean, using the polynomial division algorithm.