Let $(S,+)$ be a nontrivial commutative monoid and $R$ be a ring.
Prove that $R$ embeds in $R[X;S]$ via $a \to aX^0$
I'm not exactly sure how to approach this... I think I may need to use the fact that $R \subseteq R[X;S]$
Is that fact obvious because a monoid ring is constructed from a ring and a monoid so $R[X;S]$ is constructed by the ring $R$ and monoid $S$? How can I use that fact in the proof though?