Some results on the sum-annihilating essential submodule graph

Consider a commutative ring R with a non-zero identity ۱\neq ۰, and let M be a non-zero unitary module over R. In this document, our goal is to present the sum-annihilating essential submodule graph \mathbb{AE}^{۰}_{R}(M) and its subgraph \mathbb{AE}^{۱}_{R}(M) of a module M over a commutative ring R which is described in the following way: The vertex set of graph \mathbb{AE}^{۰}_{R}(M) (resp., \mathbb{AE}^{۱}_{R}(M)) is the collection of all (resp., non-zero proper) annihilating submodules of M and two separate annihilating submodules N and K are connected anytime N+K is essential in M. We study and investigate the basic properties of graphs \mathbb{AE}^{i}_{R}(M) (i=۰, ۱) and will present some related results. Additionally, we explore how the properties of graphs interact with the algebraic structures they represent.

کلیدواژه ها:

Annihilating submodule ، Essential submodule ، Graphs of submodules