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arXiv · 1508.02929

On the codimension of subalgebras of the algebra of matrices over a field

Giuseppe Zito
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Abstract

In this paper we provide an elementary and easy proof that a proper subalgebra of the matrix algebra $ \mathbb{K}^{n,n }$, with $n \geq3$ and $\mathbb{K}$ an arbitrary field, has dimension strictly less than $n^2-1$.

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Giuseppe Zito. 2015-09-29. On the codimension of subalgebras of the algebra of matrices over a field. https://arxiv.org/abs/1508.02929

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