Submodule is free of finite rank implies R principal ideal domain
111307
If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.
84149
Prove that an infinite ring with finite quotient rings is an integral domain
112045
A property of minimal prime ideal
85915
Principal prime ideals are minimal among prime ideals in a UFD
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
24224
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
43103
Unique factorization domain and principal ideals
78380
Dedekind domain with a finite number of prime ideals is principal
78626
Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.
80679
Principal ideal rings that are not integral domains
6646
A (non-artificial) example of a ring without maximal ideals
12474
Does an injective endomorphism of a finitely-generated free R-module have nonzero determinant?
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
89271
If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
90889
Prime ideals in a finite direct product of rings
70872
Isomorphism of quotient modules implies isomorphism of submodules?
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree