## The nilpotence bound in matrix rings

Let $F$ be a field and let $n$ be a positive integer. Does there exist an integer $k$ such that $A^k = 0$ whenever $A\in M_n(F)$ is nilpotent? Here, $M_n(F)$ denotes the ring of $n\times n$ square matrices with entries in $F$. Such an integer exists. For any nilpotent matrix $A$, we have $A^p = […]