If $\bar{k}\supseteq R\supseteq k$, then $R$ is a field?
28313
Intermediate ring between a field and an algebraic extension.
34670
What exactly is the fixed field of the map $t\mapsto t+1$ in $k(t)$?
16643
A slick proof that a field which is finitely generated as a ring is finite
79725
Fields of arbitrary cardinality
27021
Show that $Q[\sqrt3]$ is a field
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
133561
show that if $K$ is a field then $K[x]$ is principal
124511
The set of algebraic numbers is a field.
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
106737
A problem on field extension
136770
Any field that contains the integers contains the rationals as a subfield (Analysis proof)
19671
Does the "field" over which a vector space is defined have to be a Field?
138826
To show that either $R$ is a field or $R$ is a finite ring with prime number of elements and $ab = 0$ for all $a,b \in R$.
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
122415
How to show every field is a Euclidean Domain.
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field