On the matrix ring over a finite field (Q1073882)

In a previous paper by the same author [Math. Ann. 171, 79-80 (1967; Zbl 0153.062)], it is shown that if R is a ring with a finite number \(m>1\) of zero divisors, then R is finite and the number o(R) of elements in R satisfies \(o(R)\leq m^ 2\). In the present paper the author looks specifically at the ring R of \(n\times n\) matrices over a finite field and establishes (for \(n\geq 2)\) the inequality \(o(R)<m^{1+1/n(n-1)}\).