integral domain with a field as a subring
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
3604
If F is a field, then $F[x,y]$ is a Principal Ideal Domain?
151978
Splitting field of x^3-2 as a simple extension
141410
Injective integral domains are fields
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
23721
Prove that the Gaussian Integer's ring is a Euclidean domain
98540
If $F[x]$ is a principal domain does $F$ have to be necessarily a field?
65091
Subring which is not an ideal?
17859
Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
78950
Does this map extend to a unique automorphism of the polynomial ring of an integral domain?
153589
Integral basis of an extension of number fields
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?
93118
How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
128550
Algebraic field extension and intermediate integral domain
21747
A subring of the field of fractions of a PID is a PID as well.
71102
Subfields of $\mathbb{C}$ which are connected with induced topology
16984
Finite extension of domains : preimage of non-zero ideal is non-zero?