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arXiv · 2010.09220

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

Hiba F. Fayoumi
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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 $x\not=y$ 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.

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BibTeXRIS

Hiba F. Fayoumi. 2020-10-19. Locally-zero Groupoids and the Center of Bin(X). https://doi.org/10.4134/ckms.2011.26.2.163

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