1. bookVolumen 30 (2022): Heft 1 (February 2022)
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
1844-0835
Erstveröffentlichung
17 May 2013
Erscheinungsweise
1 Hefte pro Jahr
Sprachen
Englisch
access type Uneingeschränkter Zugang

On characterization of finite modules by hypergraphs

Online veröffentlicht: 12 Mar 2022
Volumen & Heft: Volumen 30 (2022) - Heft 1 (February 2022)
Seitenbereich: 231 - 246
Eingereicht: 09 May 2021
Akzeptiert: 31 Jul 2021
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
1844-0835
Erstveröffentlichung
17 May 2013
Erscheinungsweise
1 Hefte pro Jahr
Sprachen
Englisch
Abstract

With a finite R-module M we associate a hypergraph ūĚíěūĚí•‚ĄčR(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 ‚ą© L ‚Ȇ = 0 and Ei is maximal with respect to this property. We investigate some general properties of ūĚíěūĚí•‚ĄčR(M), providing condition under which ūĚíěūĚí•‚ĄčR(M) is connected, and find its diameter. Besides, we study the form of the hypergraph ūĚíěūĚí•‚ĄčR(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 ūĚíěūĚí•‚ĄčR(M).

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‚Äď304.10.1515/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‚Äď101.10.1007/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‚Äď468.10.1007/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

Empfohlene Artikel von Trend MD

Planen Sie Ihre Fernkonferenz mit Scienceendo