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THE PROBABILITY OF ZERO MULTIPLICATION IN FINITE RINGS

Part of: Radicals and radical properties of rings Conditions on elements Chain conditions, growth conditions, and other forms of finiteness

Published online by Cambridge University Press:  24 January 2022

DAVID DOLŽAN Open the ORCID record for DAVID DOLŽAN [Opens in a new window]
DAVID DOLŽAN*
Affiliation:
Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, SI-1000 Ljubljana, Slovenia
*
e-mail: david.dolzan@fmf.uni-lj.si
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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.

Keywords

finite ringzero divisorprobability

MSC classification

Primary: 16P10: Finite rings and finite-dimensional algebras
Secondary: 16N40: Nil and nilpotent radicals, sets, ideals, rings 16U99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 1 , August 2022 , pp. 83 - 88
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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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