EL-hyperstructures associated to n-ary relations
- 96 Downloads
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.
Compliance with ethical standards
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