Work

The Zero Product Probability of Some Finite Ring of Matrices Based on the Order of the Annihilator

Year: 2025

Type: article

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.

Source: Journal of the Indonesian Mathematical Society

DOI: 10.22342/jims.v31i2.1838

Authors: Nurhidayah Zaid, Nor Haniza Sarmin, Sanhan Muhammad Salih Khasraw

Institutions: Universiti Teknologi MARA, University of Technology Malaysia, Salahaddin University-Erbil

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Universiti Teknologi MARA

OpenAlex ID: W4411296555

FWCI:

Cites:

Cited by:

Related to: 10