How many ring homomorphism are there from $\mathbb{Z} / 12\mathbb{Z}$ to $\mathbb{Z} / 20\mathbb{Z}$? Find the image and kernel of them.
5699
The number of ring homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$
146341
Finding all ring homomorphisms from a field to itself
17239
Find all ideals of ${\mathbb{Z}_n}$
118073
Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
64048
Describe all ring homomorphisms
92517
Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
140865
Rings' second isomorphism theorem
63447
Prove that the kernel of a homomorphism is a principal ideal. (Artin, Exercise 9.13)
30327
$\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
34234
Kernel of injective group homomorphism
126644
Simple module and homomorphisms
84132
Number of preimages of a group element under a homomorphism.
84114
Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
55900
Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
75315
How to prove that homomorphism from field to ring is injective or zero?
34990
Ring homomorphism defined on a field
120971
(Revised) Prove that $\phi$ is a group homomorphism and find the kernel.