Subring of a field extension is a subfield
24247
Ring Inside an Algebraic Field Extension
31451
Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID
83100
Prove that the center of a ring is a subring.
115541
Subrings of polynomial rings over the complex plane
144245
Shorter proof of $R/I$ is a field if and only if $I$ is maximal
143219
If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
59347
Do extension fields always belong to a bigger field?
100162
Minimal polynomial over an extension field divides the minimal polynomial over the base field
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
65091
Subring which is not an ideal?
56551
Multiplicative group of field extension over base field
25793
Extension fields isomorphic to fields of matrices
82576
Intersection of two subfields of the Rational Function Field in characteristic $0$
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
20218
Is this field extension finite?
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?