| We investigate the interaction between a ring R and the Cayley graph Cay(L(R)) of the semigroup of left ideals of R,as well as subdigraphs of this graph.Graph theoretic properties of these graphs are investigated,such as transitive closure,girth,radius,diameter,and spanning subgraphs.Conditions on certain of these graphs are given which imply that R is regular,left duo,or that the idempotents of R are central.We characterize simple rings in terms of Cay(L(R)).We characterize strongly regular rings in terms of a subdigraph of Cay(L(R)). |
