a survey on the intersection graphs of ideals of rings

let l(r) denote the set of all non-trivial left ideals of a ring r. the intersection graph of ideals of a ring r is an undirected simple graph denoted by g(r) whose vertices are in a one-to-one correspondence with l(r) and two distinct vertices are joined by an edge if and only if the corresponding left ideals of r have a non-zero intersection. the ideal structure of a ring re ects many ring theoretical properties. there is so much research that has been conducted during the last decade to explore the properties of g(r). this is a survey of the developments in the study on the intersection graphs of ideals of rings since its introduction in 2009.