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Han, Jeong Soon; Kim, Hee Sik; Neggers, J.

The hypergroupoid semigroups as generalizations of the groupoid semigroups. (English) Zbl 1255.20061

J. Appl. Math. 2012, Article ID 717698, 8 p. (2012).
Summary: We introduce the notion of hypergroupoids \((H\text{Bin}(X),\square)\), and show that \((H\text{Bin}(X),\square)\) is a super-semigroup of the semigroup \((\text{Bin}(X),\square)\) via the identification \(x\leftrightarrow\{x\}\). We prove that \((H\text{Bin}^*(X),\ominus,[\varnothing])\) is a BCK-algebra, and obtain several properties of \((H\text{Bin}^*(X),\square)\).

MSC:

20N20 Hypergroups
20N02 Sets with a single binary operation (groupoids)
08A02 Relational systems, laws of composition
03G25 Other algebras related to logic

Keywords:

hypergroupoid semigroups; groupoid semigroups; semigroups of binary systems
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\textit{J. S. Han} et al., J. Appl. Math. 2012, Article ID 717698, 8 p. (2012; Zbl 1255.20061)
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References:

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