Coderivations of ranked bigroupoids. (English) Zbl 1255.20067

Jun, Young Bae; Lee, Kyoung Ja; Park, Chul Hwan

J. Appl. Math. 2012, Article ID 626781, 8 p. (2012).

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

Keywords:

ranked bigroupoids; generalized coderivations; rankomorphisms

References:

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