On the probability and graph of some finite rings of matrices

• Main Authors: Zaid, Nurhidayah, Sarmin, Nor Haniza, Salih Khasraw, Sanhan Muhammad
• Format: Conference or Workshop Item
• Language: English
• Published: 2020
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/90860/1/NurhidayahZaid2020_OntheProbabilityandGraphofSomeFinite.pdf; http://eprints.utm.my/id/eprint/90860/; http://dx.doi.org/10.1063/5.0018067

The study on probability theory in finite rings has been an interest of various researchers. One of the probabilities that has caught their attention is the probability that two elements of a ring have product zero. In this study, the probability is determined for a finite ring R of matrices over integers modulo four. First, the annihilators of R are determined with the assistance of Groups, Algorithms and Programming (GAP) software and then the probability is calculated using the definition. Next, by using the results obtained, the zero divisor graph of the ring R is constructed. A zero divisor graph is defined as a graph in which the zero divisors of R are its vertices and two vertices are connected by an edge if their product is zero.