Why is the one-variable ring of polynomials with real coefficients a principal ideal domain?
133561
show that if $K$ is a field then $K[x]$ is principal
78626
Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.
117536
Why is the localization at a prime ideal a local ring?
70047
Is the ideal generated by irreducible element in principal ideal domain maximal?
87331
Real polynomial in two variables
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
123024
A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
79041
What is the formal definition of polynomial ring of several variables?
141078
Domain over which a polynomial is strictly positive
78950
Does this map extend to a unique automorphism of the polynomial ring of an integral domain?
121986
Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?
43103
Unique factorization domain and principal ideals
89056
Intuitive understanding of ideal $I = (x+1,x^2+1)$ and the quotient $\Bbb Z[x]/I$
23721
Prove that the Gaussian Integer's ring is a Euclidean domain
104782
Polynomial irreducible - maximal ideal
34754
Why is the polynomial ring of more than one variable not a PID?
89313
Maximal ideals of polynomial rings in infinitely many variables