Say $R$ is a commutative ring. Does there exists a subring of $R[x]$ that is isomorphic to $R$?
My approach would be to define the subring of $R[x]$ that generates $R$. Any thoughts?
Hint $ $ The evaluation hom $\rm\:f(x)\to f(0)\:$ is $1$-$1$, onto, restricted to polynomials of degree zero.