MHB What Are the Coefficients in Aluffi's Monoid Rings?

[Math Amateur]

I am reading Paolo Aluffi's book, Algebra: Chapter 0.

I have a question related to Aluffi's description of monoid rings ... ...

In Chapter III, Section 1.4 on monoid rings, we read the following:View attachment 4476
View attachment 4477

In the above text we find:"Given a monoid $$(M, \cdot )$$ and a ring $$R$$, we can obtain a new ring $$R[M]$$ as follows.Elements of $$R[M]$$ are formal linear combinations

$$\sum_{ m \in M} a_m \cdot m $$

where the 'coefficients' $$r_m$$ are formal elements of $$R$$ and $$a_m \ne 0$$ for at most finitely many summands ... ... "
My question is as follows:What are the $$r_m$$ exactly and what is their relation to the a_m ... ?Is it a typo ... that is does Aluffi mean .." ... ... where the 'coefficients' $$a_m$$ are formal elements of $$R$$ ... " ... that is ... does he mean $$a_m$$ where he writes $$r_m$$?Hope someone can clarify this issue for me ... ...

Peter

 

[Fallen Angel]

Hi Peter,

I'm pretty sure that it's a typo, read it as $a_{m}$.

 

[Math Amateur]

Hi Peter,

I'm pretty sure that it's a typo, read it as $a_{m}$.

Thanks Fallen Angel ... certainly thought it might be ... but was not completely confident that I was not missing something ...

Thanks again,

Peter