Resumen de A generalization of the annihilating ideal graph for modules

Soraya Barzegar, Saeed Safaeeyan, Ehsan Momtahan

• 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 a module of finite length with finitely many maximal submodules. We also derive necessary and sufficient conditions for the annihilating submodule graph of a reduced module to be bipartite (resp., complete bipartite). Finally, we present an algorithm for deriving both Γ(Zn) and G(Zn) by Maple, simultaneously.