Let R be a commutative ring with 1. Let M₂(R) be the 2 × 2 matrix ring over R and R[x] be the polyno- mial ring over R. Consider the subsets
s= a b |a,b€R and J= 0 b |a,b €R
0 a 0 0
of M₂ (R), and consider the function : R[x] → M₂(R) given for any polynomial p(x) = co+c₁x+...+c₂x² € R[x] by
∅(p(x)0=c0 c1
0 c0
(4) Give an example of R for which J is a prime ideal of S but not a maximal ideal of S. Explain your answer.