  We define the finite number ring ${\Bbb Z}_n [\sqrt [m] r]$ where $m,n$ are
positive integers and $r$ in an integer akin to the definition of the Gaussian
integer ${\Bbb Z}[i]$. This idea is also introduced briefly in [7]. By
definition, this finite number ring ${\Bbb Z}_n [\sqrt [m] r]$ is naturally
isomorphic to the ring ${\Bbb Z}_n[x]/{\langle x^m-r \rangle}$. From an
educational standpoint, this description offers a straightforward and
elementary presentation of this finite ring, making it suitable for readers who
do not have extensive exposure to abstract algebra. We discuss various
arithmetical properties of this ring. In particular, when $n=p$ is a prime
number and $\mathbb{Z}_p$ contains a primitive $m$-root of unity, we describe
the structure of $\mathbb{Z}_n[\sqrt[m]{r}]$ explicitly.
