논문KCI 등재
Locally-zero groupoids and the center of Bin(X)
대한수학회 (The Korean Mathematical Society)|2011.04|대한수학회논문집 (Communications of the KMS)|제26권 제2호|pp. 163-168
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In this paper we introduce the notion of the center ZBin(X) in the semigroup Bin(X) of all binary systems on a set X, and show that if (X, (기호) ) ∈ ZBin(X), then x≠y implies {x,y}={x(기호)y,y(기호)x}. Moreover, we show that a groupoid (X,(기호) )∈ ZBin(X) if and only if it is a locally-zero groupoid.
Abstract
In this paper we introduce the notion of the center ZBin(X) in the semigroup Bin(X) of all binary systems on a set X, and show that if (X, (기호) ) ∈ ZBin(X), then x≠y implies {x,y}={x(기호)y,y(기호)x}. Moreover, we show that a groupoid (X,(기호) )∈ ZBin(X) if and only if it is a locally-zero groupoid.
참고문헌 (5)
- R. H. Bruck, "A Survey of Binary Systems" (1958), Springer-Verlag
- Hee Sik Kim, "The semigroups of binary systems and some perspectives", 대한수학회보, 45(4), pp.651~661 (2008), 대한수학회
- L. Nebesky, "An algebraic characterization of geodetic graphs", Czechoslovak Math. J, 48(4), pp.701~710 (1998)
- L. Nebesky, "A tree as a nite nonempty set with a binary operation", Math. Bohem, 125(4), pp.455~458 (2000)
- L. Nebesky, "Travel groupoids", Czechoslovak Math. J, 56(2), pp.659~675 (2006)
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