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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 H R is a hypergroup. It proves that if H R is a hypergroup, S is an extension of R contained in the transitive closure of R and \( S \subset \) S 2, then H S is also a hypergroup. Corollaries for various extensions of R, the union, intersection and product constructions being employed, are then proved. If H R and H S 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.

Keywords

Binary Relation Transitive Closure Iterative Sequence Product Construction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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