*The applications of zero divisors of some finite rings of matrices in probability and graph theory.*
Jurnal Teknologi, 83 (1).
pp. 127-132.
ISSN 2180–3722
(2021)

## Abstract

Let R be a finite ring. The zero divisors of R are defined as two nonzero elements of R, say x and y where xy = 0. Meanwhile, the probability that two random elements in a group commute is called the commutativity degree of the group. Some generalizations of this concept have been done on various groups, but not in rings. In this study, a variant of probability in rings which is the probability that two elements of a finite ring have product zero is

determined for some ring of matrices over integers modulo n. The results are then applied into graph theory, specifically the zero divisor graph. This graph is defined as a graph where its vertices are zero divisors of R and two distinct

vertices x and y are adjacent if and only if xy = 0. It is found that the zero divisor graph of R is a directed graph.

Item Type: | Article |
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Keywords: | Graph Theory, Zero divisor, Ring theory, Ring of matrices, Zero divisor graph |

Taxonomy: | By Subject > Computer & Mathematical Sciences > Statistics |

Local Content Hub: | Subjects > Computer and Mathematical Sciences |

Depositing User: | Muslim Ismail @ Ahmad |

Date Deposited: | 22 Feb 2022 23:27 |

Last Modified: | 22 Feb 2022 23:27 |

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