Is the only homomorphism $\phi:\mathbb{R} \rightarrow \mathbb{R}$ onto the ring of reals the identity?
30817
Is an automorphism of the field of real numbers the identity map?
6825
If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
55900
Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
91222
Isomorphism between $\mathfrak o(4,\mathbb R)$ and $\mathfrak o (3,\mathbb R) \oplus\mathfrak o (3,\mathbb R) $
67237
Pull back image of maximal ideal under surjective ring homomorphism is maximal
131946
Order of an Element Under a Homomorphism
146341
Finding all ring homomorphisms from a field to itself
112131
Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
157378
On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions
57732
Rings of fractions and homomorphisms
30714
A question on ring homomorphisms and maximal ideals.
153291
Why a ring homomorphism from a local ring will not map a non-unit to a unit？
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
144105
Ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is always identity or $0$
129162
Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
101064
Showing the triviality of homomorphisms