$A[x]$ is a commutative domain if and only if $A$ is a commutative domain
8317
Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
23242
Commutative integral domain with d.c.c. is a field
151018
Proving that any finite integral domain is a field.
76661
Checking the maximality of a principal ideal in $R[x]$
1580
An integral domain $A$ is exactly the intersection of the localisations of $A$ at each maximal ideal
81982
Is $\mathbb{Z}[x]$ a principal ideal domain?
44405
Prove XOR is commutative and associative?
90599
Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
24224
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
123024
A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
139463
Commutative integral domain does not finitely generate its field of fractions
90314
Maximal ideals in $R[x]$
122958
$R/I$ is commutative iff $rs-sr \in I$
3604
If F is a field, then $F[x,y]$ is a Principal Ideal Domain?
76432
$i^{-1} F$ a sheaf if and only if $\varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U) \to F_x \times F_y$ is an isomorphism.