For a commutative ring $\mathbb{M}$ and ideal $\mathbb{A}$, let $N(A)$={x in M|there exists a non-negative integer $ n $ such that $x^{n}$ in $\mathbb{A}$}. Which of following is true for $N(A)=A$?
I. $M=\mathbb Z, A=(2)$
II. $M= \mathbb Z[x]$, $A=(x^{2}+2)$
III. $M= \mathbb Z/27 \mathbb Z, A=(18+27 \mathbb Z)$