[SOLVED] rings with unity 1. The problem statement, all variables and given/known data Corollary 27.18 (in Farleigh) 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_n with n not equal to m? If it is possible, give an example. If it is impossible, prove it. EDIT: change the second Z_n to Z_m 2. Relevant equations 3. The attempt at a solution My intuition tells me it is impossible. But I have no idea how to prove it.