4-adic numbers and zero divisors

If one defines the $4$-adic numbers as the inverse limit $$\Bbb Z_4\cong\lim_{\longleftarrow}(\Bbb Z/4^n\Bbb Z)$$ then $\Bbb Z_4\cong\Bbb Z_2$, the $2$-adic numbers.

In general $\Bbb Z_{p^k}\cong\Bbb Z_p$.