Subfield of $\mathbb{R}$ such that $\Bbb R/K$ is finite.
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
126552
Number of subfields of finite field
74663
Is $\mathbb{R}$ an algebraic extension of some proper subfield?
150170
Subrings of fraction fields
92677
Infinite algebraic extension of a finite field
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
144245
Shorter proof of $R/I$ is a field if and only if $I$ is maximal
63280
Show that the set $\mathbb{Q}[\sqrt{2}] = \{a + b \sqrt{2} \mid a, b \in \mathbb{Q}\}$ is a field with the usual multiplication and addition.
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
71102
Subfields of $\mathbb{C}$ which are connected with induced topology
157585
Structure theorem of finite rings
36044
Show $\Bbb R ^n$ with a finite set removed is still connected.
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
84830
Vector space of infinite sequences in $\Bbb R$
58424
If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.
13606
Prove that $K$ is isomorphic to a subfield of the ring of $n\times n$ matrices over $F$.
45627
Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$