1. bookVolumen 30 (2022): Edición 1 (February 2022)
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1844-0835
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17 May 2013
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On characterization of finite modules by hypergraphs

Publicado en línea: 12 Mar 2022
Volumen & Edición: Volumen 30 (2022) - Edición 1 (February 2022)
Páginas: 231 - 246
Recibido: 09 May 2021
Aceptado: 31 Jul 2021
Detalles de la revista
License
Formato
Revista
eISSN
1844-0835
Primera edición
17 May 2013
Calendario de la edición
1 tiempo por año
Idiomas
Inglés
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).

Keywords

MSC 2010

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