An integral domain $R$ with fraction field $K$ satisfying this property is a local ring?
57198
How to show that a valuation ring has a unique maximal ideal?
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
93118
How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
151423
Is there a nice description of the field of fractions of the ring of polynomials with integer coefficients?
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
141410
Injective integral domains are fields
3936
Characterization of valuation rings
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree
48818
Homomorphism of local rings
74139
Subrings of integral domains have the same identity element.
135152
Non-UFD integral domain such that prime is equivalent to irreducible?
129184
Krull dimension of this local ring
155991
Is it the case that every quotient ring ${F[x]}/{(p(x))}$ is a PID?
29359
Localisation isomorphic to a quotient of polynomial ring
112099
Polynomial ring with integral coefficients is integral