Let $A$ be the ring of all entire functions under point-wise addition and multiplication. Then which of the following are true?\\
(A) $A$ does not have non-zero nilpotent elements.\\
(B) In the group of the units of $A$ (under multiplication), every element other than 1 has infinite order.\\
(C) For every $f \in A$, there is a sequence of polynomials which converges to $f$ uniformly on compact sets.\\
(D) The ideal generated by $z$ and $\sin z$ is principal.