Group homomorphism is also ring homomorphism
129858
"Almost" ring homomorphism
1026
Ring homomorphism with $\phi(1_R) \neq1_S$
2153
How to get a homomorphism from $\mathbb{Z}\to G$, for $G$ a non-trivial group?
64048
Describe all ring homomorphisms
83710
Order of a homomorphism of groups
62454
Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.
106347
Why is the image of a homomorphism a subgroup of the codomain?
55900
Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
642
Does a surjective ring homomorphism have to be surjective on the unit groups?
40383
Is it true that $|g| = |\phi(g)|$ for all homomorphisms $\phi: G \to G$ and $g \in G$?
120971
(Revised) Prove that $\phi$ is a group homomorphism and find the kernel.
61334
Application of Main Homomorphism Theorem
1558
Number of homomorphisms between two cyclic groups.
57732
Rings of fractions and homomorphisms
34599
Number of ring homomorphisms from $\mathbb Z_{12}$ to $\mathbb Z_{28}$.
35961
In what sense of "structure" do group homomorphisms "preserve structure"?
54911
The preimage of a normal subgroup under a group homomorphism is normal