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> Let $m,n\in\mathbb{N}:\gcd(m,n)=1$ prove there is no $M\_n(\mathbb{C})$-module $V$ s.t. $\dim\_{\mathbb{C}}V=m$
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I think that since $V$ is an $M\_n(\mathbb{C})$-module we should have that $\dim\_{\mathbb{C}}V\mid n$ and thus we are done but is that really correct? If so how can I prove it?