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 $$S[x]$$.