If $F$ is a field and $\phi:F[x] \to F[x]$ is a ring automorphism,with the property that $\forall \lambda \in F:\phi (\lambda)=\lambda$
121244
Homomorphisms and automorphisms on polynomial rings
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
98540
If $F[x]$ is a principal domain does $F$ have to be necessarily a field?
133561
show that if $K$ is a field then $K[x]$ is principal
103491
If $A$ is a semilocal ring and $f:A\rightarrow B$ is a surjective homomorphism, then $f(\operatorname{rad}A)=\operatorname{rad}B$
40678
Image of an ideal under a surjective ring homomorphism is an ideal
133627
If $\phi(g)=g^3$ is a homomorphism and $3 \nmid |G|$, $G$ is abelian.
62615
If F is a finite field, then $F^F=P_F$.
60760
Ring homomorphism and characteristic
3604
If F is a field, then $F[x,y]$ is a Principal Ideal Domain?
13606
Prove that $K$ is isomorphic to a subfield of the ring of $n\times n$ matrices over $F$.
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
78835
An automorphism of the field of $p$-adic numbers
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
149856
Image of ring homomorphism is a subring
1026
Ring homomorphism with $\phi(1_R) \neq1_S$
109039
Does this "extension property" for polynomial rings satisfy a universal property?