The Hypergroupoid Semigroups as Generalizations of the Groupoid Semigroups

Abstract

We introduce the notion of hypergroupoids (𝐻Bin(𝑋),□), 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),□).