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The Scientific World Journal
Volume 2014 (2014), Article ID 726470, 6 pages
Research Article

-Step Derivations on -Groupoids: The Case

1Department of Mathematics, King Abdulaziz University, Faculty of Science for Girls, Jeddah, Saudi Arabia
2Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea
3Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA

Received 11 February 2014; Accepted 19 May 2014; Published 8 July 2014

Academic Editor: Xiao-Long Xin

Copyright © 2014 N. O. Alshehri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We define a ranked trigroupoid as a natural followup on the idea of a ranked bigroupoid. We consider the idea of a derivation on such a trigroupoid as representing a two-step process on a pair of ranked bigroupoids where the mapping is a self-derivation at each step. Following up on this idea we obtain several results and conclusions of interest. We also discuss the notion of a couplet on , consisting of a two-step derivation and its square , for example, whose defining property leads to further observations on the underlying ranked trigroupoids also.