Koh, Kwangil On the matrix ring over a finite field. (English) Zbl 0589.16016 Linear Algebra Appl. 66, 195-197 (1985). 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 \(o(R)<m^{1+1/n(n-1)}\). Reviewer: J.Brawley, jun Cited in 1 ReviewCited in 1 Document MSC: 16P10 Finite rings and finite-dimensional associative algebras 16S50 Endomorphism rings; matrix rings Keywords:matrix rings; zero divisors Citations:Zbl 0153.062 PDFBibTeX XMLCite \textit{K. Koh}, Linear Algebra Appl. 66, 195--197 (1985; Zbl 0589.16016) Full Text: DOI References: [1] Koh, K., On properties of rings with a finite number of zero divisors, Math. Ann., 171, 79-80 (1967) · Zbl 0153.06201 [2] Rotman, J. J., The Theory of Groups (1968), Allyn and Bacon: Allyn and Bacon Boston This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.