Order related concepts for arbitrary groupoids
Bull. Korean Math. Soc. 2017 Vol. 54, No. 4, 1373-1386
https://doi.org/10.4134/BKMS.b160593
Published 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  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd