Which of the following rings are integral domains?
(a) $\{a+b\sqrt{5}:a,b\in \mathbb{Q}\}$
(b) the ring of continuous functions from $[0,1]$
(c) the polynomial ring $\mathbb{Z}[x]$.
(d) the ring of complex analytic functions on the disc $\{z\in\mathbb{C}: |z|<1\}$
I know that (a) and (c) are integral domain. i also see in Wikipedia that (b) is not a integral domain but I cannot find any counter example.
For (d) I have no idea.
Can anyone help me please.