A generalization of the annihilating ideal graph for modules
A generalization of the annihilating ideal graph for modules
We show that an R-module M is noetherian (resp., artinian) if and only if its annihilating submodule graph, G(M ), is a non-empty graph and it has ascending chain condition (resp., descending chain condition) on vertices.Moreover, we show that if G(M ) is a locally finite graph, then M is …