Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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n-ARY HYPERGROUPS ASSOCIATED WITH n-ARY RELATIONS

  • Received : 2011.10.26
  • Published : 2013.03.31
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Abstract

The notion of $n$-ary algebraic hyperstructures is a generalization of ordinary algebraic hyperstructures. In this paper, we associate an n-ary hypergroupoid (H, $f$) with an ($n+1$)-ary relation ${\rho}_{n+1}$ defined on a non-empty set H. Then, we obtain some basic results in this respect. In particular, we investigate when it is an $n$-ary $H_v$-group, an $n$-ary hypergroup or a join $n$-ary space.

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