EL-hyperstructures associated to n-ary relations
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This contribution deals with n-ary relations and hyperstructure theory. There exists a way of creating semihypergroups and hypergroups from (partially) quasi-ordered (semi)groups known as Ends lemma construction. In this paper, we use this method to introduce a new class of (semi)hypergroup from a given (semi)group endowed with a preordering n-ary relation as a generalization of EL-hyperstructures. Then, we study some basic properties and important elements belonging to this class and the essential differences between this new class and the earlier one (i.e. EL-hyperstructures) are also investigated.
KeywordsEnds lemma EL-hyperstructure (semi)hypergroup n-ary relation
The authors are highly grateful to the referees for their valuable comments and suggestions for improving the paper.
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Conflict of interest
The authors declare that there are no conflicts of interest in this paper.
- Chvalina J (1995) Functional graphs, quasi-ordered sets and commutative hypergroups. Masaryk University, Brno (in Czech)Google Scholar
- Gutan C (1991) Simplifiable semihypergroups. Algebraic hyperstructures and applications, (Xanthi, 1990), 103–111. World Scientific Publishing, TeaneckGoogle Scholar
- Hošková S (2008a) Binary hyperstructures determined by relational and transformation systems. Habilitation thesis, Faculty of Science, University of OstravaGoogle Scholar
- Hošková S (2008b) Order hypergroups-The unique square root condition for quasi-order hypergroups. Set Valued Math Appl 1:1–7Google Scholar
- Hošková S, Chvalina J (2008c) Discrete transformation hypergroups and transformation hypergroups with phase tolerance space. Discrete Math. 308(18):43–54Google Scholar
- Hu J, Chen L, Qiu S, Liu M (2014) A new approach for n-ary relationships in object databases. Conceptual modeling. Springer International Publishing, New YorkGoogle Scholar
- Marty F (1934) Sur une generalization de la notion de groupe, In: Proceedings of 8th Congres des Mathematiciens Scandinaves, StockholmGoogle Scholar
- Novák M (2012) EL-hyperstructures: an overview. Ratio Math. 23:65–80Google Scholar
- Novák M (2011) Important elements of EL-hyperstructures. In: APLIMAT: 10th International Conference, STU in Bratislava, Bratislava, pp 151–158Google Scholar
- Novák M (2010) The notion of subhyperstructure of “Ends lemma”-based hyperstructures. Aplimat J Appl Math 3(II):237–247Google Scholar
- Novák M (2015) On EL-semihypergroups. Eur J Combin Part B 44:274–286Google Scholar
- Račkova P (2008) Hypergroups of symmetric matrices. In: Proceedings of 10th international congress of algebraic hyperstructures and applications (AHA)Google Scholar
- Rosenberg IG (1998) Hypergroups and join spaces determined by relations. Ital J Pure Appl Math 4:93–101Google Scholar
- Vougiouklis T (1987) Generalization of P-hypergroups. Rend Circ Mat. Palermo 36(II):114–121Google Scholar
- Zielinsky B (2015) Generalised n-ary relations and allegories in relational and algebraic methods in computer science. Springer International Publishing, ChamGoogle Scholar