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http://dx.doi.org/10.4134/CKMS.2011.26.2.163

LOCALLY-ZERO GROUPOIDS AND THE CENTER OF BIN(X)  

Fayoumi, Hiba F. (Department of Mathematics University of Alabama)
Publication Information
Communications of the Korean Mathematical Society / v.26, no.2, 2011 , pp. 163-168 More about this Journal
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,${\bullet}$) ${\in}$ ZBin(X), then x ${\neq}$ y implies {x,y}=${x{\bullet}y,y{\bullet}x}$. Moreover, we show that a groupoid (X,${\bullet}$) ${\in}$ ZBin(X) if and only if it is a locally-zero groupoid.
Keywords
center; locally-zero; Bin(X);
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 0
연도 인용수 순위
1 L. Nebesky, An algebraic characterization of geodetic graphs, Czechoslovak Math. J. 48(123) (1998), no. 4, 701-710.
2 L. Nebesky, A tree as a finite nonempty set with a binary operation, Math. Bohem. 125 (2000), no. 4, 455-458.
3 L. Nebesky, Travel groupoids, Czechoslovak Math. J. 56(131) (2006), no. 2, 659-675.
4 R. H. Bruck, A Survey of Binary Systems, Springer-Verlag, New York, 1958.
5 H. S. Kim and J. Neggers, The semigroups of binary systems and some perspectives, Bull. Korean Math. Soc. 45 (2008), no. 4, 651-661.   과학기술학회마을   DOI   ScienceOn