مشخصات پژوهش

Let R be a commutative ring with identity. We consider a simple graph associated with R, denoted by Ω∗ R, whose vertex set is the set of all non-trivial ideals of R and two distinct vertices I and J are adjacent whenever JAnn(I) = (0) or IAnn(J) = (0). In this paper, we characterize the commutative Artinian non-local ring R for which Ω∗ R has genus one and crosscap one.