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

Abstract

In this paper we provide an elementary and easy proof that a proper subalgebra of the matrix algebra ${\mathbb{K}}^{n,n}$, with $n\ge 3$ and $\mathbb{K}$ an arbitrary field, has dimension strictly less than $n^2-1$.

5 pages. Comments welcome

References in corpus (1)

• The maximal dimension of unital subalgebras of the matrix algebra