Let $R$ be a ring. Since $R$ is also a group then we can talk about the group ring $R[R]$. I want to understand this group ring $R[R]$.
An element $x\in R[R]$ is written as a finite formal sum $$x=r_1s_1+r_2s_2+\cdots+r_ns_n$$ where both $r_i$ and $s_i$ are in $R$ but since the ring $R$ is closed under sum and multiplication, then it is clear that $x\in R$. So can't we just say that the group ring $R[R]$ is equal to $R$?