# n-ARY HYPERGROUPS ASSOCIATED WITH n-ARY RELATIONS

• Momeni, Somayyeh
• Published : 2013.03.31
• 54 4

#### 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.

#### Keywords

hypergroup;binary relation;n-ary hypergroup;n-ary $H_v$-group;join n-ary space

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#### Cited by

1. n–ary hyperstructures constructed from binary quasi–ordered semigroups vol.22, pp.3, 2014, https://doi.org/10.2478/auom-2014-0056
2. Semihypergroups associated with ternary relations vol.29, pp.3-4, 2018, https://doi.org/10.1007/s13370-018-0554-8