If $R$ is an Euclidean domain that is not a field, is $R[X]$ a PID?
78626
Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
136855
Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
7011
Integral domain with fraction field equal to $\mathbb{R}$
78950
Does this map extend to a unique automorphism of the polynomial ring of an integral domain?
141477
Decomposition of finitely generated graded modules over PID
57592
Does existence of $\gcd$ implies PID?
47975
Closed cone in the euclidean space $\mathbb{R}^n$
62134
Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
17859
Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
102914
Integral domain that is not a factorization domain
119866
Subring of PID is also a PID?
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
551
Why is a finite integral domain always field?
96132
$R$ integral domain : $u\in R^*, a \text{ is prime} \iff au \text{ is prime}$
5594
Question about the Euclidean ring definition
119056
If in a UFD every maximal ideal is principal then it is a PID