Semi-Neutral Groupoids And BCK-algebras Commun. Korean Math. Soc. Published online October 13, 2021 HeeSik Kim, Joseph Neggers, and YoungJoo Seo Hanyang University; Alabama University; Daejin University Abstract : We study the notion of a left-almost-zero groupoid, and we generalize two axioms which play important roles in the theory of BCK-algebras using the notion of a projection. Moreover, we investigate a Smarandache disjointness of semi-leftoids. Keywords : left-almost-zero, semi-(neutral, leftoid), power associative, BCK-algebra, trace function, projection, Smarandache disjoint MSC numbers : 20N02, 06F35 Full-Text :