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We introduce the notion of hypergroupoids (HBinX,□), and show that (HBin(X),□) is a super-semigroup of the semigroup (Bin(X),□) via the identification x↔{x}. We prove that (HBin*(X),⊖,[∅]) is a BCK-algebra, and obtain several properties of (HBin*(X),□).

The Hypergroupoid Semigroups as Generalizations of the Groupoid Semigroups