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Coderivations of ranked bigroupoids. (English) Zbl 1255.20067
Summary: The notion of (co)derivations of ranked bigroupoids is discussed by N. O. Alshehri, H. S. Kim, and J. Neggers [Derivations on ranked bigroupoids. Appl. Math. Inf. Sci. (to appear)], and their generalized version is studied by Y. B. Jun, E. H. Roh, and G. Muhiuddin [Generalized derivations on ranked bi-groupoids. Knowl.-Based Syst. (to appear)]. In particular, Y. B. Jun et al. [loc. cit.] studied coderivations of ranked bigroupoids. In this paper, the generalization of coderivations of ranked bigroupoids is discussed. The notion of generalized coderivations in ranked bigroupoids is introduced, and new generalized coderivations of ranked bigroupoids are obtained by combining a generalized self-coderivation with a rankomorphism. From the notion of \((X,*,\&)\)-derivation, the existence of a rankomorphism of ranked bigroupoids is established.
MSC:
20N99 Other generalizations of groups
08A02 Relational systems, laws of composition
06F35 BCK-algebras, BCI-algebras (aspects of ordered structures)
16W25 Derivations, actions of Lie algebras
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