The polynomial ring $R[x]$ is the <a href="keywords/keyword/35/">monoid ring</a> of the monoid $\Bbb N$ of nonnegative integers over a ring $R$. The polynomial ring $R[X]$, where $X$ is a set of variables (possibly infinite), is the monoid ring of the direct sum $\bigoplus\limits_{x \in X} \Bbb N$.
Rings with this keyword