Q: Right socle of a group ring Let $p$ be a prime number and $n$ a positive integer. I want to know what is the (right) socle of the group ring $A=\mathbb Z_{(p)}C_n$, where $\mathbb Z_{(p)}$ is the localization of integers at the prime ideal $(p)$, and $C_n$ is the cyclic group of order $n$. Thanks for any help!

A: It's zero. If $M$ is any non-zero right ideal, then $pM$ is a strictly smaller right ideal, so there are no minimal right ideals.
