Could $E$ have a subfield of order 8
116616
Could $X^3 + X + 1$ have a root in $E?$
20218
Is this field extension finite?
126127
A field extension of prime degree
123419
Abstract algebra: homomorphism and an element of a prime order
155125
Every ordered field has a subfield isomorphic to $\mathbb Q$?
31961
Given fields $M/E/F$, why does $[M:F] = [M:E][E:F]$?
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
138279
Multiplicative order and powers
57846
Multiplicative inverse in $\operatorname{GF}(2^8)$?
113411
If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?
140144
Can you find an element of order 10 in $\mathbb{Z}_{31}^{*}$
74681
A finite extension with finitely many intermediate fields is simple
81844
How would you show that field automorphisms fix prime subfields?
22158
Find the quadratic sub field of $\mathbb Q(\zeta_7)$ which can be expressed in the form $\mathbb Q(\sqrt D)$,where $D$ is an integer.
143615
Can you construct a field with 4 elements?
26398
Group of even order contains an element of order 2
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?