Answer to Question #23456 in Abstract Algebra for jeremy
For any integer n > 0, show that
is a prime ring.
To see that R is prime, viewit as a subring of P = M2(Z). Note that nP ⊆ R. If a, b ∈ R are such that aRb = 0, then naPb ⊆ aRb = 0, and hence aPb = 0. Since P isa prime ring, we conclude that a = 0 or b = 0.