n-ARY HYPERGROUPS ASSOCIATED WITH n-ARY RELATIONS

Title & Authors
n-ARY HYPERGROUPS ASSOCIATED WITH n-ARY RELATIONS

Abstract
The notion of $\small{n}$-ary algebraic hyperstructures is a generalization of ordinary algebraic hyperstructures. In this paper, we associate an n-ary hypergroupoid (H, $\small{f}$) with an ($\small{n+1}$)-ary relation $\small{{\rho}_{n+1}}$ defined on a non-empty set H. Then, we obtain some basic results in this respect. In particular, we investigate when it is an $\small{n}$-ary $\small{H_v}$-group, an $\small{n}$-ary hypergroup or a join $\small{n}$-ary space.
Keywords
hypergroup;binary relation;n-ary hypergroup;n-ary $\small{H_v}$-group;join n-ary space;
Language
English
Cited by
1.
n–ary hyperstructures constructed from binary quasi–ordered semigroups, Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2014, 22, 3
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