For which numbers $l \leq |K|$ field $K$ has subfield, which has $l$ elements?
6855
Subfields of finite fields
134773
A domain is a field if it has a common multiple $\!\neq\! 0$ of all elements $\!\neq\! 0$
13606
Prove that $K$ is isomorphic to a subfield of the ring of $n\times n$ matrices over $F$.
23712
$F$ is a finite field of size $s$. Prove that if $s=2^m$ for some $m>0$, then all elements of F have a square root.
147069
Intersection of field extensions
87467
Finding some missing subfields of a splitting field of $x^4-7$
70776
Characteristic of a field is $0$ or prime
147200
Given fields $K\subseteq L$, why does $f,g$ relatively prime in $K[x]$ imply relatively prime in $L[x]$?
60212
algebraic element over a field
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
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
18048
Easy criteria to determine isomorphism of fields?
153589
Integral basis of an extension of number fields
119758
On the order of elements of $\mathrm{GL}(2,q)$.
134896
Enlightening proof that the algebraic numbers form a field
5069
$GL_n(\mathbb F_q)$ has an element of order $q^n-1$
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?