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Zaid, Nurhidayah
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Mathematics

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The Zero Product Probability of Some Finite Ring of Matrices Based on the Order of the Annihilator Zaid, Nurhidayah; Sarmin, Nor Haniza; Khasraw, Sanhan Muhammad Salih
Journal of the Indonesian Mathematical Society Vol. 31 No. 2 (2025): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i2.1838

Abstract

An annihilator is defined as the set of pairs of elements in a ring R in which the product of the elements in the pair is the zero element of R. In this paper, we aim to determine the order of the annihilator of the finite ring of matrices of dimension two over integers modulo prime, M2(Zp). The order of the annihilator is determined by using number theory, specifically the linear congruence method. Another subject that we discuss in this paper is the zero product probability of a finite ring. The zero product probability is defined as the probability that two elements of a finite ring have product zero. Based on the order of the annihilator, the general formula of the zero product probability of M2(Zp) is determined.
Co-Authors Khasraw, Sanhan Muhammad Salih Sarmin, Nor Haniza