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On the matrix ring over a finite field. (English) Zbl 0589.16016

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

MSC:

16P10 Finite rings and finite-dimensional associative algebras
16S50 Endomorphism rings; matrix rings

Citations:

Zbl 0153.062
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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
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