n-hypergroups and binary relations

  • Authors:
  • V. Leoreanu-Fotea;B. Davvaz

  • Affiliations:
  • Faculty of Mathematics, "Al.I. Cuza" University, 6600 Iaşi, Romania;Department of Mathematics, Yazd University, Yazd, Iran

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2008

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Abstract

In this paper, we introduce and study the notion of a partial n-hypergroupoid, associated with a binary relation. Some important results concerning Rosenberg partial hypergroupoids, induced by relations, are generalized to the case of n-hypergroupoids. Then, n-hypergroups associated with union, intersection, products of relations and also mutually associative n-hypergroupoids are analyzed. Finally, n-hypergroupoids associated with relations are used in order to study the transitivity of the relation @b in n-semihypergroups.