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Rings with a few more zero-divisors

Published online by Cambridge University Press:  17 April 2009

C. Christensen
C. Christensen
Affiliation:
Department of Pure Mathematics, School of General Studies, Australian National University, Canberra, ACT.
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Abstract

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It is well-known that every finite ring with non-zero-divisors has order not exceeding the square of the order n of its left zero-divisor set. Unital rings whose order is precisely n2 have been described already. Here we discuss finite rings with relatively larger zero-divisor sets, namely those of order greater than n3/2. This is achieved by describing the class of all finite rings with left composition length two at most, and using a theorem relating the left composition length of a finite ring to the size of its left zero-divisor set.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 2 , October 1971 , pp. 271 - 274
Copyright
Copyright © Australian Mathematical Society 1971

References

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