• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.209-216
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• 2002

We study correspondences between interval structures and hyperstructures.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.553-573
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• 2000

In this paper, we consider hyperstructures (H,·) when H={e,a,b}. We put a condition on (H,·) where e is a unit. We obtain minimal and maximal Hv -groups , semigroups and quasigroups , using Mathematical 3.0 computer programs.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.233-245
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• 2019

Cyclic hypergroups are of great importance due to their applications to many field in mathematics. In this paper, we classify all polygroups of order less than six where each of its non-identity elements is a generator.

• 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.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.401-413
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• 2002

In this paper, we consider hyperstructures (H,.) defined on the set H = {e, a, b}. We study the hyperstructure of H when every element is one of a scalar unit, a unit or a weak scalar. On those conditions the $H_{\upsilon}$-quasigroups are classified. And we obtain the 15 minimal $H_{\upsilon}$-groups and 2 non-quasi $H_{\upsilon}$-semigroups For these we use the Mathematica 3.0 computer programs.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.2
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• pp.9-17
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• 2001

Vogiouklis introduced $H_v$-hyperstructures and gave the "open problem: for $H_v$-groups, we have ${\beta}^*={\beta}^{\prime\prime}$. We have an affirmative result about this open problem for some special cases. We study ${\beta}$ relations on $H_v$-quasigroups. When a set H has at least three elements and (H, ${\cdot}$) is an $H_v$-quasigroup with a weak scalar e, if there are elements $x,y{\in}H$ such that xy = H \ {e}, then we have (xy)(xy) = H.