# 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.

R =

Z nZ

Z Z

is a prime ring.

Expert's answer

To see that

*R*is prime, viewit as a subring of*P*= M_{2}(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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