Idempotents of ${\mathbb{Z}}_n$

Abstract

We know that if there are $k$ distinct prime factors of $n\in \mathbb{N}$, then the ring ${\mathbb{Z}}_n$ of integers modulo $n$ has exactly $2^k$ idempotent elements. In this article, we try to describe all the idempotents of ${\mathbb{Z}}_n$ for any given $n\in \mathbb{N}$.

13 pages