When Intersection Ideals of Graphs of Rings are a Divisor graph

Abstract

Let R be a commutative principal ideal ring with unity. In this paper, we classify when the intersectiongraphs of ideals of a ring R G(R), is a divisor graph. We prove that the intersection graphs of ideals of a ring RG(R), is a divisor graph if and only if R is a local ring or it is a product of two local rings with each of them hasone chain of ideals. We also prove that G(R), is a divisor graph if it is a product of two local rings one of themhas at most two non-trivial ideals with empty intersection.

Studying structure of Coronaviridae, analyzing their geometry and focusing on the role of electronic applications in health awareness of viruses

“…All of us know the fundamental notions of geometry which we deal with every day such as distance, length, area, volume, point, line, ray, plane, angle, shape, surface, curve and manifolds. Symmetry and multitude of forms of symmetric patterns in surfaces that occur in nature are important because it is a kind of transformation and geometric transformation that takes straight lines into straight lines and curves into curves which are responsible of forming new surfaces from old, congruences like those in COVID-19 and rigid motions like in Figure 3 (Al-Labadi, 2020).…”