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http://dx.doi.org/10.4134/BKMS.2013.50.2.507

n-ARY HYPERGROUPS ASSOCIATED WITH n-ARY RELATIONS  

Anvariyeh, Seid Mohammad (Department of Mathematics Yazd University)
Momeni, Somayyeh (Department of Mathematics Yazd University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 507-524 More about this Journal
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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