Let I be an ideal of a commutative ring R with unity. If I is a prime ideal,show that I[x] is a prime ideal of R[x].

Let I be an ideal of a commutative ring R with unity. If I is a prime ideal,show that I[x] is a prime ideal of R[x]. Give an example of a commutative ring with unity and a maximal ideal I of R such that I[x] is not a maximal ideal of R[x].