If there exist a non-trivial algebra homomorphism from $M_n(\mathbb R)$ to $M_m(\mathbb R)$, prove $n|m$
I find that the homomorphism is injective because $M_n(\mathbb R)$ is simple,but i dont know what should i do next
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$\begingroup$ What is Mm(R)? Which homomorphism? Please define/add details for clarity. And use mathjax to your question. Here is a link for a tutorial: math.meta.stackexchange.com/questions/5020/… $\endgroup$– Timon KoltCommented Sep 5 at 7:52
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