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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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