Communications of the
Korean Mathematical Society CKMS

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