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.
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