Prove that set of all non principal ideals of an integral domain has a maximal element
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
151018
Proving that any finite integral domain is a field.
80679
Principal ideal rings that are not integral domains
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
102914
Integral domain that is not a factorization domain
87078
Prove the following set is an ideal of the ring $Z[x]$
60674
Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
104377
Maximal Ideals in Ring of Continuous Functions
116000
Prove that prime ideals of a finite ring are maximal
22544
Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
110022
Showing prime and maximal ideal
134991
Commutative non Noetherian rings in which all maximal ideals are finitely generated
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
6646
A (non-artificial) example of a ring without maximal ideals
24224
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
141659
Every field is an integral domain