| Autor: |
Zaid, Nurhidayah, Sarmin, Nor Haniza, Khasraw, Sanhan Muhammad Salih |
| Předmět: |
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| Zdroj: |
AIP Conference Proceedings; 2024, Vol. 3189 Issue 1, p1-6, 6p |
| Abstrakt: |
A zero divisor graph of a finite ring is defined as a simple graph with its vertices are the zero divisors of the ring, and two distinct vertices are adjacent if and only if their product is equal to the zero element of the ring. In this research, the zero divisor graph is identified for the ring of 2 × 2 matrices over integers modulo prime. Since the ring is noncommutative, the zero divisor graph is a directed graph. First, the vertices of the graph are determined by obtaining the zero divisors of the ring based on its definition. Then, the arcs of the graph are determined by finding the set of annihilators of the ring, which is stated as the set of pairs of elements in the ring where their product is zero. In this research, we define a new term called the square-annihilator. The set of square-annihilators is the set of pairs of the same element where their product is zero. To ensure the zero divisor graph is simple, the elements of the square-annihilators are eliminated from the original set of annihilators. Thus, the general formula for the number of vertices and arcs of the zero divisor graph are obtained. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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