An extension of the essential graph of a ring

• Дата: 2024
• Автори: Ali, Asma, Ahmad, Bakhtiyar
• Формат: Стаття
• Мова: English
• Опубліковано: Lugansk National Taras Shevchenko University 2024
• Теми: zero-divisor graph; essential graph; reduced ring; 13A15; 05C99; 05C25.
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2120
• Назва журналу: Algebra and Discrete Mathematics

Let \(A\) be a commutative ring with non-zero identity, and \(E(A)=\{p\in A | ann_A(pq)\leq_e A, ~\mbox { for some } ~q\in A^* \}\) . The extended essential graph, denoted by \(E_gG(A)\) is a graph with the vertex set \(E(A)^*=E(A)\setminus\{0\}\). Two distinct vertices \(r, s\in E(A)^*\) are adjace...