Prove that the kernel is a principal ideal
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
85915
Principal prime ideals are minimal among prime ideals in a UFD
104789
How to tell an ideal of integer polynomial ring is principal?
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
76661
Checking the maximality of a principal ideal in $R[x]$
156858
Kernel of powers of a normal operator
23037
Computing the order of $\mathrm{SL}_2(\mathbb F_p)$ as the kernel of $\mathrm{GL}_2(\mathbb F_p)$
133561
show that if $K$ is a field then $K[x]$ is principal
54360
Injective implies trivial kernel.
93658
Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
146801
Primary decomposition of an ideal
48291
Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
70047
Is the ideal generated by irreducible element in principal ideal domain maximal?
33245
Show that every ideal of the ring $\mathbb Z$ is principal
145351
Ring of formal power series over a principal ideal domain is a unique factorisation domain
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.