Locally-zero Groupoids and the Center of Bin(X)

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 $x\ne y$ 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.

6 pages; http://koreascience.or.kr/article/JAKO201115037885418.pdf