Let $R$ be an integral domain which is not a field. Then can $R[x]$ have a maximal ideal generated by a non-constant polynomial?
76661
Checking the maximality of a principal ideal in $R[x]$
74537
Maximal Ideals in $K[y]$
119699
Examples of Cohen-Macaulay integral domains
11259
Prove $R\times S$ is not an integral domain
112099
Polynomial ring with integral coefficients is integral
108896
Prime ideal in a polynomial ring over an integrally closed domain
46040
Preimage of maximal ideal is maximal (why is this answer wrong?)
3604
If F is a field, then $F[x,y]$ is a Principal Ideal Domain?
90314
Maximal ideals in $R[x]$
30714
A question on ring homomorphisms and maximal ideals.
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
94819
Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
151794
Can an ideal in a commutative integral domain be its own square?
104377
Maximal Ideals in Ring of Continuous Functions
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.