Continuing Exercise 25, is it possible that a ring with unity may simultaneously contain two subrings isomorphic to the fields Z_p and Z_q for two different primes p and q? Give an example or prove it is impossible.

Data from Exercise 25

Corollary 27.18 tells us that every ring with unity contains a subring isomorphic to either Z or some Z_n. Is it possible that a ring with unity may simultaneously contain two subrings isomorphic to Z_n and Z_m for n ≠ m? If it is possible, give an example. If it is impossible, prove it.