Left rays of groupoids

Abstract

In this paper, we introduce and study the notion of a (positive implicative) left ray in groupoids, and we show that every normal subgroup of a group is a left ray of a group, and in every finite group, left rays are normal subgroups. Further, left absorptive subsets of groupoids are discussed and several examples for these definitions provided. The relationship between left rays and zero semigroups is discussed.