It's well known that, given a basis $b\in\mathbb N$, $b\ge2$, then each $x\in\mathbb N$, $x\ne0$ admits a unique decomposition as a sum
$$x=\sum_{k=0}^n a_kb^k,$$
where $a_k\in\{0,1,\dots,b-1\}$ for all $0\le k\le n$ and $n=n(x)$ is the biggest $n\in\mathbb N$ such that $x\ge b^n$.
Question: is there an analogous of that fact for some class of (semi)rings, instead of $\mathbb N$ ?