# Answer to Question #17112 in Abstract Algebra for Tsit Lam

Question #17112

Let R, S be rings such that Mm(R) ∼= Mn(S). Does this imply that m = n and R ∼ S?

Expert's answer

The answer is “no”. For instance,for

*R*= M2(Q) and*S*= M3(Q), we have*R is not isomorphic to**S*(by dimension considerations), but M3(*R*)*∼*= M2(*S*) since both rings are isomorphic to M6(Q).
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