In an integral domain $R$, are principal ideas always equal to $R$ ??
551
Why is a finite integral domain always field?
83871
GCDs in integral domains are unique up to unit factors (associates)
21202
Axiom of choice is equivalent to every relation includes a function with the same domain
31049
If $p$ is an irreducible element of an integral domain $D$, and if $e$ belongs to $D^\ast$ prove that $ep$ is also ireducible
89271
If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
54957
The necessary and sufficient condition for a unit element in Euclidean Domain
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
1580
An integral domain $A$ is exactly the intersection of the localisations of $A$ at each maximal ideal
124672
Let $f:R\rightarrow S$ be a ring homomorphism. Prove or disprove: if $f$ is onto and $R$ is an integral domain, then $S$ is an integral domain
134458
Isomorphisms preserving integral domains and fields
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
512
Finding generator for the ideal generated by $a$ and $b$ in an euclidean domain
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.
147722
Is there a nice example of integral domain $R$ and $s,t \in R$, with $Rs \cap Rt$ not principal but lcm($s,t$) exists?
102914
Integral domain that is not a factorization domain
141410
Injective integral domains are fields