Zaid, N. and Sarmin, N. H. (2021) The applications of zero divisors of some finite rings of matrices in probability and graph theory. Jurnal Teknologi, 83 (1). ISSN 01279696

PDF
594kB 
Official URL: http://dx.doi.org/10.11113/jurnalteknologi.v83.149...
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 

Uncontrolled Keywords:  graph theory, ring of matrices, ring theory 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  94600 
Deposited By:  Narimah Nawil 
Deposited On:  31 Mar 2022 15:12 
Last Modified:  31 Mar 2022 15:12 
Repository Staff Only: item control page