Bulletin of the
Korean Mathematical Society BKMS

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.

Keywords: hypergroup, binary relation, $n$-ary hypergroup, $n$-ary $H_{v}$-group, join $n$-ary space

MSC numbers: 20N20