1. bookTom 30 (2022): Zeszyt 1 (February 2022)
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License
Format
Czasopismo
eISSN
1844-0835
Pierwsze wydanie
17 May 2013
Cz─Östotliwo┼Ť─ç wydawania
1 raz w roku
J─Özyki
Angielski
access type Otwarty dost─Öp

On characterization of finite modules by hypergraphs

Data publikacji: 12 Mar 2022
Tom & Zeszyt: Tom 30 (2022) - Zeszyt 1 (February 2022)
Zakres stron: 231 - 246
Otrzymano: 09 May 2021
Przyj─Öty: 31 Jul 2021
Informacje o czasopi┼Ťmie
License
Format
Czasopismo
eISSN
1844-0835
Pierwsze wydanie
17 May 2013
Cz─Östotliwo┼Ť─ç wydawania
1 raz w roku
J─Özyki
Angielski
Abstract

With a finite R-module M we associate a hypergraph ­Łĺ×­ŁĺąÔäőR(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 Ôłę L Ôëá = 0 and Ei is maximal with respect to this property. We investigate some general properties of ­Łĺ×­ŁĺąÔäőR(M), providing condition under which ­Łĺ×­ŁĺąÔäőR(M) is connected, and find its diameter. Besides, we study the form of the hypergraph ­Łĺ×­ŁĺąÔäőR(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 ­Łĺ×­ŁĺąÔäőR(M).

Keywords

MSC 2010

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