### Homomorphisms, Kernels and Prime Ideals

Given an onto ring homomorphism Φ: R1 --> R2 we saw in class that if I <u>C</u> R1 is an ideal containing the kernel of Φ, then Φ(I) is an ideal of R2. In addition, we saw that if J <u>C</u> R2 is an ideal, then Φˉ¹(J) is an ideal of R1 containing kernel of Φ. (i) Show that if I <u>C</u> R1 is a