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THE PROBABILITY OF ZERO MULTIPLICATION IN FINITE RINGS

Published online by Cambridge University Press:  24 January 2022

DAVID DOLŽAN*
Affiliation:
Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, SI-1000Ljubljana, Slovenia

Abstract

Let R be a finite ring and let ${\mathrm {zp}}(R)$ denote the nullity degree of R, that is, the probability that the multiplication of two randomly chosen elements of R is zero. We establish the nullity degree of a semisimple ring and find upper and lower bounds for the nullity degree in the general case.

Type
Research Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The author acknowledges financial support from the Slovenian Research Agency (research core funding no. P1-0222).

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