The effect of assuming the identity as a generator on the length of the matrix algebra

Thomas Laffey, Olga Markova, Helena Šmigoc

Let $M_n(\mathbb{F})$ be the algebra of $n\times n$ matrices and let $\mathcal{S}$ be a generating set of $M_n(\mathbb{F})$ as an $\mathbb{F}$-algebra. The length of a finite gener…