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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