Ring Theory/Ring extensions

Note that if $S/R$ is a ring extension, then $S[x]/R[x]$ is a ring extension; indeed, the set $S[x]$ is the set of all polynomials with coefficients in $S$, the set $R[x]$ is the set of all polynomials with coefficients in $R$, and $R[x]$ is a subring of $S[x]$.