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Answer to Question #23456 in Abstract Algebra for jeremy

Question #23456
For any integer n > 0, show that
R =
Z nZ
Z Z
is a prime ring.
Expert's answer
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.

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