Q:

Ring theory (about prime ideal)

How can we find the number of prime ideals of $Z_{10^5}$ ? It has been asked that the number of prime ideal of $Z_{10^5}$ is 
$a) 2
$
$b) 5
$
$c) 10
$
$d) 10000$

A:

You just compute the number of prime ideals in $\mathbb{Z}$ containing $10^5\mathbb{Z}$. Since $a\mathbb{Z}\supseteq b\mathbb{Z}$ if and only if $a\mid b$…

