Pick out the correct statements from the following list:
a. A homomorphic image of a UFD (unique factorization domain) is again a UFD.
b. The element $2 ∈ \Bbb{Z}[\sqrt{−5}]$ is irreducible in $\Bbb{Z}[\sqrt{−5}].$
c. Units of the ring $\Bbb{Z}[\sqrt{−5}]$ are the units of $\Bbb{Z}.$
d. The element $2$ is a prime element in $\Bbb{Z}[\sqrt{−5}].$
I think (d) is not correct. But I'm not sure about the others.