• 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.

• 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.