(n − 1) -Step Derivations on n-Groupoids: The Case n=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 d is a self-derivation at each step. Following up on this idea we o...

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Bibliographic Details
Published in:TheScientificWorld 2014-01, Vol.2014 (2014), p.1-6
Main Authors: Alshehri, Noura Omair, Neggers, J., Kim, Hee Sik
Format: Article
Language:English
Subjects:
Group theory
Mathematical research
Mathematics
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Summary: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.
ISSN:2356-6140
1537-744X
1537-744X
DOI:10.1155/2014/726470