A question in definition of group rings

Question

In definition of a group ring $RG$ with elements $∑f_g g$ (where $g\in G$ and $f_g\in R$), are we supposed that $f_g$'s commute with $g$'s? I mean could we identify the above formal summation with $∑ gf_g$? This question arises when working with an involution $*$ in $RG$ where $(ab)^*=b^*a^*$ for $a,b\in RG$. Thanks to anybody answering!

Answer 1

Yes.

The elements of G commute with those of R in the group ring.