Research Article ( − 1)-Step Derivations on -Groupoids: The Case = 3

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

Further Results on Derivations of Ranked Bigroupoids

Further properties on (X,∗,&)-self-(co)derivations of ranked bigroupoids are investigated, and conditions for an (X,∗,&)-self-(co)derivation to be regular are provided. The notion of ranked ∗-subsystems is introduced, and related properties are investigated