title: (n - 1)-Step derivations on n-groupoids: the case n = 3.
abstract: 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 d 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 (D, d) on X, consisting of a two-step derivation d and its square D = d ∘ d, for example, whose defining property leads to further observations on the underlying ranked trigroupoids also.
authors.affiliation: Department of Mathematics, King Abdulaziz University, Faculty of Science for Girls, Jeddah, Saudi Arabia.
authors.forename: N O
authors.initials: NO
authors.lastname: Alshehri
authors.affiliation: Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea.
authors.forename: Hee Sik
authors.identifier: 0000-0001-5321-5919
authors.initials: HS
authors.lastname: Kim
authors.affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA.
authors.forename: J
authors.initials: J
authors.lastname: Neggers