Need help in showing that $\mathbb{Z}_{m}$ is a principal ideal ring

Question

I'm asked to show that $\mathbb{Z}_m$ (the integers mod $m$) is a principal ideal ring for every $m > 0$

I see that it is the same discussion used in verifying that $\mathbb{Z}$ (the set of all integers) is.

Can anybody help me in writing a correct solution?

Answer 1

Use that $\Bbb Z_m$ is a quotient of $\Bbb Z$. In general, the residues of the generators of an ideal generate the image of the ideal in the quotient.