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\(H_ v\)-groups defined on the same set. (English) Zbl 0855.20057

A hypergroupoid \((H,)\) is called weakly associative if \((xy)z\cap x(yz)\neq\emptyset\), for every \(x\), \(y\) and \(z\) in \(H\). If \(xH=H=Hx\), for every \(x\in H\), the hypergroupoid is said to be a quasihypergroup. An element \(e\in H\) is called a scalar unit if \(ex=x=xe\), for every \(x\in H\).
In this paper all the weakly associative quasihypergroups having a scalar unit and defined on a set with three elements are determined.

MSC:

20N20 Hypergroups
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References:

[1] Corsini, P., Prolegomena of hypergroup theory, (1992), Aviani Editore · Zbl 0785.20032
[2] Marty, F., Sur une generalisation de la notion de groupe, (), 45-49 · JFM 61.1014.03
[3] Vougiouklis, T., A new class of hyperstructures, J. combin. inf. system sci., 20, 229-235, (1995) · Zbl 0874.20052
[4] Vougiouklis, T., Groups in hypergroups, Ann. discrete math., 37, 459-468, (1988)
[5] Vougiouklis, T., The fundamental relation in hyperrings, (), 203-211 · Zbl 0763.16018
[6] Vougiouklis, T., The set of hypergroups with operators which are constructed from a set with two elements, Acta un. carolinae math. phys., 22, 7-10, (1981) · Zbl 0493.20052
[7] Vougiouklis, T., The very thin hypergroups and the S-construction, (), 471-477 · Zbl 0945.20524
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