(n-1)-Step Derivations on n-Groupoids: The Case n=3

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Date
2014
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi
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 circle d, for example, whose defining property leads to further observations on the underlying ranked trigroupoids also.

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Keywords
LATTICES, Multidisciplinary Sciences
Citation
Alshehri, N. O., Kim, H. S., & Neggers, J. (2014). <mml:math xmlns:mml='http://www.w3.org/1998/Math/MathML' id='M1'><mml:mi>(n</mml:mi><mml:mo>−</mml:mo><mml:mn>1)</mml:mn></mml:math>-Step Derivations on<mml:math xmlns:mml='http://www.w3.org/1998/Math/MathML' id='M2'><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math>-Groupoids: The Case<mml:math xmlns:mml='http://www.w3.org/1998/Math/MathML' id='M3'><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:math>. In The Scientific World Journal (Vol. 2014, pp. 1–6). Hindawi Limited. https://doi.org/10.1155/2014/726470