Let $R$ be a non zero ring with identity. Clearly $R[x]$ embeds in $R[[x]]$. Is it true that for any $n$, one can embed $R[x_1,...,x_n]$ in $R[[x]]$ ?
Yes. Take algebraically independent power series $a_1(x),\dots, a_n(x)$ and map $x_i$ to $a_i$. For example, one can take $a_1(x) = x$, $a_2(x) = \exp(x)$, $a_3(x) = \exp(\exp(x))$, ... 

