1. bookVolume 30 (2022): Edizione 1 (February 2022)
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Formato
Rivista
eISSN
1844-0835
Prima pubblicazione
17 May 2013
Frequenza di pubblicazione
1 volta all'anno
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Inglese
access type Accesso libero

On characterization of finite modules by hypergraphs

Pubblicato online: 12 Mar 2022
Volume & Edizione: Volume 30 (2022) - Edizione 1 (February 2022)
Pagine: 231 - 246
Ricevuto: 09 May 2021
Accettato: 31 Jul 2021
Dettagli della rivista
License
Formato
Rivista
eISSN
1844-0835
Prima pubblicazione
17 May 2013
Frequenza di pubblicazione
1 volta all'anno
Lingue
Inglese
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

[1] S. Akbari, H.A. Tavallaee, S. Khalashi Ghezelahmad, Intersection graph of submodules of a module, J. Algebra Appl., 11 (2012), 1250019.10.1142/S0219498811005452 Search in Google Scholar

[2] S. Akbari, H.A. Tavallaee, S. Khalashi Ghezelahmad, On the complement of the intersection graph of submodules of a module, J. Algebra Appl., 14 (2015), 1550116.10.1142/S0219498815501169 Search in Google Scholar

[3] S. Akbari, H.A. Tavallaee, S. Khalashi Ghezelahmad, Some results on the intersection graph of submodules of a module, Math. Slovaca 67(2) (2017), 297–304.10.1515/ms-2016-0267 Search in Google Scholar

[4] C. Berge. Graphes and hypergraphes, 1970. Dunod, Paris, 1967. Search in Google Scholar

[5] C. Berge. Graphs and hypergraphs, volume 7. North-Holland publishing company Amsterdam, 1973. Search in Google Scholar

[6] A. Haouaoui, A. Benhissi, The k-zero-divisor hypergraph, Ricerche di Matematica, 61 (2012), 83–101.10.1007/s11587-011-0117-x Search in Google Scholar

[7] K. Selvakumar, V. Ramanathan, Classification of non-local rings with projective 3-zero-divisor hypergraph, Ricerche di Matematica, 66 (2017), 457–468.10.1007/s11587-016-0313-9 Search in Google Scholar

[8] V. Voloshin, Introduction to Graph and Hypergraph Theory. Nova Science Publ., 2009. Search in Google Scholar

[9] D. B. West, Introduction to Graph Theory, 2nd edn. (Prentice Hall, 2001). Search in Google Scholar

[10] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Reading, 1991. Search in Google Scholar

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