In a normal extension of a field, is there an automorphism that maps irreducible factors of a certain irreducible polynomial?
97024
If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.
37593
Can all real polynomials be factored into quadratic and linear factors?
36965
Automorphism of rational numbers
148909
Irreducible polynomials of degree 3 and 5
106629
Trace map from finite surjective morphism of normal irreducible varieties
14270
Polynomial divisibility is unchanged by coeff. field extension
100162
Minimal polynomial over an extension field divides the minimal polynomial over the base field
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
80188
There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
78835
An automorphism of the field of $p$-adic numbers
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
118610
Are all extensions of finite fields cyclic?
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
55432
Infinite distinct factorizations into irreducibles for an element
78950
Does this map extend to a unique automorphism of the polynomial ring of an integral domain?
30817
Is an automorphism of the field of real numbers the identity map?
64878
Is this polynomial irreducible in $\mathbb{Q}$?