The Hypergroupoid Semigroups as Generalizations of the Groupoid Semigroups

Abstract

We introduce the notion of hypergroupoids (HBin(X), square), and show that (HBin(X), square), is a super-semigroup of the semigroup (Bin(X), square), via the identification x <-> {x}. We prove that (HBin*(X), circle minus, [empty set]) is a BCK-algebra, and obtain several properties of (HBin*(X), square).