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 Order related concepts for arbitrary groupoids Bull. Korean Math. Soc. 2017 Vol. 54, No. 4, 1373-1386 https://doi.org/10.4134/BKMS.b160593Published online July 31, 2017 Hee Sik Kim, Joseph Neggers, and Keum Sook So Hanyang University, University of Alabama, Hallym University Abstract : In this paper, we introduce and explore suggested notions of above', below' and `between' in general groupoids, $Bin(X)$, as well as in more detail in several well-known classes of groupoids, including groups, semigroups, selective groupoids (digraphs), $d/BCK$-algebras, linear groupoids over fields and special cases, in order to illustrate the usefulness of these ideas. Additionally, for groupoid-classes (e.g., $BCK$-algebras) where these notions have already been accepted in a standard form, we look at connections between the several definitions which result from our introduction of these ideas as presented in this paper. Keywords : below, above, between, $d/BCK$-algebra, poset, $Bin(X)$, order-preserving, $\beta$-medial MSC numbers : Primary 20N02, 20M10, 06A06 Downloads: Full-text PDF