The Image of a Natural Number in a Commutative Ring

In the setting of The Natural Numbers and the Natural Numbers with Zero: Arithmetic, Order, Induction and Recursion, let $R$, with $+$, $\cdot$, $0$ and $1$, be a commutative ring, and let $n\in\mathbb{N}_{0}$, with $[n]$ as in Intervals of Natural Numbers §segment.

¶ The image of $n$ in $R$ is $n_{R}=\sum_{k=1}^{n}1$, the finite sum of the constant map $k\mapsto1$ on $[n]$, if $n\in\mathbb{N}$; and $n_{R}=0$ if $n=0$.