Studying some semisimple modules via hypergraphs

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Hosseini Behrouz; Moniri Hamzekolaee Ali Reza

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Journal Paper

Paper Information

Journal: Algebraic structures and their applications Year:2024 | Volume:11 | Issue:4 Page(s): 311-319

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Information Journal Paper

Title

Studying some semisimple modules via hypergraphs

Author(s)

Hosseini Behrouz | Moniri Hamzekolaee Ali Reza | Issue Writer Certificate

Keywords

Hyperedge

Hypergraph

Semisimple module

Simple submodule

Small submodule

Abstract

Recent studies have shown that Hypergraphs are useful in solving real-life problems. Hypergraphs have been successfully applied in various fields. Inspiring by the importance, we shall introduce a new Hypergraph assigned to a given module. By the way, vertices of this Hypergraph (which we call sum Hypergraph) are all nontrivial submodules of a module $P$ and a subset $E$ of the vertices is a Hyperedge in case the sum of each two elements of $E$ is equal to $P$ and $E$ is maximal with respect to this condition. Some general properties of such Hypergraphs are discussed. Semisimple modules with length $2$ are characterized by their corresponding sum Hypergraphs. It is shown that the sum Hypergraph assigned to a finite module $P$ is connected if and only if $P$ is semisimple.

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