TITLE: Ring homomorphism
QUESTION [6 upvotes]: The number of non-trivial ring homomorphisms from $\mathbb{Z}_{12}$ to $\mathbb{Z}_{28}$ is
(Options:                                                                                                            a.1  b.3  c.4  d.7)

REPLY [4 votes]: To be a mere group homomorphism, then the order of the image of 1 will have to divide both 12 and 28. So that leaves four options for 1 to map to.
If it has to be a ring homomorphism, then 1 must map to an idempotent element of $\mathbb{Z}_{28}$. Only two of the four previous possibilities are idempotent.