algebra universalis

, Volume 43, Issue 4, pp 321–330 | Cite as

Hypergroups and binary relations

  • Piergiulio Corsini
  • Violeta Leoreanu

Abstract.

The paper deals with a binary relation R on a set H, where the Rosenberg partial hypergroupoid HR is a hypergroup. It proves that if HR is a hypergroup, S is an extension of R contained in the transitive closure of R and \( S \subset \)S2, then HS is also a hypergroup. Corollaries for various extensions of R, the union, intersection and product constructions being employed, are then proved. If HR and HS are mutually associative hypergroups then \( H_{R \cup S} \) is proven to be a hypergroup. Lastly, a tree \( {\Bbb T} \) and an iterative sequence of hyperoperations \( _{_\circ\atop k} \) where k = 1, 2, ...) on its vertices are considered. A bound on the diameter of \( {\Bbb T} \) is given for each k such that \( _{_\circ\atop k} \) is associative.

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Copyright information

© Birkhäuser Verlag Basel, 2000

Authors and Affiliations

  • Piergiulio Corsini
    • 1
  • Violeta Leoreanu
    • 2
  1. 1.Dipartimento di Matematica e Informatica, Via delle Scienze 206 (loc. Rizzi), I-33100 Udine, Italia, e-mail: corsini@dimi.uniud.itIT
  2. 2.Faculty of Mathematics, "Al.I. Cuza" University, 6600 Iaşi, Romania, e-mail: leoreanu@uaic.roRO

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