field extension $F(x)=F(x^2)$
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
112125
In an extension field, is there any difference between the original field and its isomorphic copy in the extension field?
85096
Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
16589
Field of fractions of integral extension is an algebraic extension
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
20218
Is this field extension finite?
122050
Algebraic extension of perfect field in which every polynomial has a root is algebraically closed
112556
When is $F(\sqrt c)$ a field?
67157
Example of an non-normal inseparable field extension
115129
Constructing an explicit isomorphism between finite extensions of finite fields
51612
Question About Notation In Field Theory $F(x)$ vs. $F[x]$
14270
Polynomial divisibility is unchanged by coeff. field extension
48093
Irreducible polynomial in field extension
128550
Algebraic field extension and intermediate integral domain
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
4178
Solve $f(x)f(2x^2) = f(2x^3+x)$