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With a finite <italic>R</italic>-module <italic>M</italic> we associate a hypergraph 𝒞𝒥ℋ<italic>R</italic>(<italic>M</italic>) having the set <italic>V</italic> of vertices being the set of all nontrivial submodules of <italic>M</italic>. Moreover, a subset <italic>Ei</italic> of <italic>V</italic> with at least two elements is a hyperedge if for <italic>K, L</italic> in <italic>Ei</italic> there is <italic>K ∩ L ≠</italic> = 0 and <italic>Ei</italic> is maximal with respect to this property. We investigate some general properties of 𝒞𝒥ℋ<italic>R</italic>(<italic>M</italic>), providing condition under which 𝒞𝒥ℋ<italic>R</italic>(<italic>M</italic>) is connected, and find its diameter. Besides, we study the form of the hypergraph 𝒞𝒥ℋ<italic>R</italic>(<italic>M</italic>) when M is semisimple, uniform module and it is a direct sum of its each two nontrivial submodules. Moreover, we characterize finite modules with three nontrivial submodules according to their co-intersection hypergraphs. Finally, we present some illustrative examples for 𝒞𝒥ℋ<italic>R</italic>(<italic>M</italic>).
</abstract>

With a finite R-module M we associate a hypergraph 𝒞𝒥ℋR(M) having the set V of vertices being the set of all nontrivial submodules of M. Moreover, a subset Ei of V with at least two elements is a hyperedge if for K, L in Ei there is K ∩ L ≠ = 0 and Ei is maximal with respect to this property. We investigate some general properties of 𝒞𝒥ℋR(M), providing condition under which 𝒞𝒥ℋR(M) is connected, and find its diameter. Besides, we study the form of the hypergraph 𝒞𝒥ℋR(M) when M is semisimple, uniform module and it is a direct sum of its each two nontrivial submodules. Moreover, we characterize finite modules with three nontrivial submodules according to their co-intersection hypergraphs. Finally, we present some illustrative examples for 𝒞𝒥ℋR(M).

On characterization of finite modules by hypergraphs

Department of Mathematics, Faculty of Mathematical Sciences

Department of Mathematics, Faculty of Basic Sciences

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On characterization of finite modules by hypergraphs"}

With a finite R-module M we associate a hypergraph 𝒞𝒥ℋR(M) having the set V of vertices being the set of all nontrivial submodules of M. Moreover, a subset...

On characterization of finite modules by hypergraphs

Published Online: Mar 12, 2022

Page range: 231 - 246

Received: May 09, 2021

Accepted: Jul 31, 2021

DOI: https://doi.org/10.2478/auom-2022-0013

Keywords
Hyperedge, hypergraph, co-intersection hypergraph

© 2022 Ali Reza Moniri Hamzekolaee et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On characterization of finite modules by hypergraphs

Published Online: Mar 12, 2022

Page range: 231 - 246

Received: May 09, 2021

Accepted: Jul 31, 2021

DOI: https://doi.org/10.2478/auom-2022-0013

KeywordsHyperedge, hypergraph, co-intersection hypergraph

© 2022 Ali Reza Moniri Hamzekolaee et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Hyperedge, hypergraph, co-intersection hypergraph