Locally-zero groupoids and the center of $Bin(X)$
Commun. Korean Math. Soc. 2011 Vol. 26, No. 2, 163-168
https://doi.org/10.4134/CKMS.2011.26.2.163
Printed June 1, 2011
Hiba F. Fayoumi
University of Alabama
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 $x\not=y$ 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, $Bin(X)$
MSC numbers : 20N02
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