On pairs of matrices generating matrix rings and their presentations

B. V. Petrenko, S. N. Sidki

Let $M_n(\mathbb{Z})$ the ring of $n$-by-$n$ matrices with integral entries, and $n\ge 2$. This paper studies the set $G_n(\mathbb{Z})$ of pairs $(A,B)\in M_n(\mathbb{Z}{)}^2$ gen…