Suppose $R$ is any commutative ring which is not a field. I am trying to show that maximal ideals of $R[X]$ should be of the form $\left<m,f(x)\right>$, where $m$ is a maximal ideal in $R$ and $f(x)$ is irreducible mod $m$.
While this particular result seems to be true when $R$ is any noetherian ring of dimension at most $1$, can someone prove in general if the result is true? Any help will be appreciated. Thanks