# Can we deduce that two rings $R_1$ and $R_2$ are isomorphic if their polynomial ring are isomorphic?

Given two rings $$R_1$$ and $$R_2$$ (with or without identity: it's not specified). If $$R_1[x]$$ is isomorphic to $$R_2[y]$$ (No such requirement that the isomorphism sends the constant terms to constant terms), can we deduce that $$R_1 \cong R_2$$?

I feel there might be a counterexample but it's quite hard to find one.