Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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LOCALLY-ZERO GROUPOIDS AND THE CENTER OF BIN(X)

  • Fayoumi, Hiba F. (Department of Mathematics University of Alabama)
  • Received : 2010.01.07
  • Published : 2011.04.30
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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.

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References

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