Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain.
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
551
Why is a finite integral domain always field?
53349
Prove that $\sqrt{x}$ is continuous on its domain $[0, \infty).$
1580
An integral domain $A$ is exactly the intersection of the localisations of $A$ at each maximal ideal
76496
Showing that every field is an integral domain.
49438
Prove that $X^\ast$ separable implies $X$ separable
33645
Proving that an integral domain has at most two elements that satisfy the equation $x^2 = 1$.
121465
$R[x]$ has a subring isomorphic to $R$.
78626
Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.
36996
If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
93118
How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
154495
Prove that a nontrivial subring of a ring that is a domain has the same identity
93658
Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
108896
Prime ideal in a polynomial ring over an integrally closed domain
84149
Prove that an infinite ring with finite quotient rings is an integral domain
24224
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
151794
Can an ideal in a commutative integral domain be its own square?