Answer to Question #23458 in Abstract Algebra for jeremy
Show that R = Z nZ Z Z is not isomorphic to the prime ring P = M2(Z) if n > 1.
Assume n > 1. To see that Ris not isomorphic P, note that, the ideals of P are of theform M2(kZ) = kM2(Z) = kP, where k∈Z. Now R has an ideal M2(nZ) (which is, infact, an ideal of the larger ring P). Since this ideal of R isobviously not of the form kR for any integer k, it follows that Ris not isomorphic P.