• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.507-524
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• 2013

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.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.513-526
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• 2010

In this paper, the theory of n-ary hypergroups and some applications of hyperalgebras (Fredholm-Voltra integral, copula) are studied. We define some new concepts of topological hyperdynamical systems, universal hyperdynamical systems and immersed universal hyperalgebra. Also, we present some results in this respect.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.515-530
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• 2015

We say that (R, f, g) is an additive (m, n)-semihyperring if R is a non-empty set, f is an m-ary associative hyperoperation, g is an n-ary associative operation and g is distributive with respect to f. In this paper, we describe a number of characterizations of additive (m, n)-semihyperrings which generalize well-known results. Also, we consider distinguished elements, hyperideals, Rees factors and regular relations. Later, we give a natural method to derive the quotient (m, n)-semihyperring.