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

Coderivations of ranked bigroupoids. (English) Zbl 1255.20067

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
16W25 Derivations, actions of Lie algebras

Keywords:

ranked bigroupoids; generalized coderivations; rankomorphisms
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\textit{Y. B. Jun} et al., J. Appl. Math. 2012, Article ID 626781, 8 p. (2012; Zbl 1255.20067)
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References:

[1] H. E. Bell and L.-C. Kappe, “Rings in which derivations satisfy certain algebraic conditions,” Acta Mathematica Hungarica, vol. 53, no. 3-4, pp. 339-346, 1989. · Zbl 0705.16021
[2] H. E. Bell and G. Mason, “On derivations in near-rings,” in Near-Rings and Near-Dields, vol. 137, pp. 31-35, North-Holland, Amsterdam, The Netherlands, 1987. · Zbl 0619.16024
[3] K. Kaya, “Prime rings with \alpha derivations,” Hacettepe Bulletin of Natural Sciences and Engineering, vol. 16-17, pp. 63-71, 1987-1988. · Zbl 0696.16031
[4] E. C. Posner, “Derivations in prime rings,” Proceedings of the American Mathematical Society, vol. 8, pp. 1093-1100, 1957. · Zbl 0082.03003
[5] Y. B. Jun and X. L. Xin, “On derivations of BCI-algebras,” Information Sciences, vol. 159, no. 3-4, pp. 167-176, 2004. · Zbl 1044.06011
[6] N. O. Alshehri, “On derivations of incline algebras,” Scientiae Mathematicae Japonicae, vol. 71, no. 3, pp. 349-355, 2010. · Zbl 1195.16048
[7] N. O. Alshehri, H. S. Kim, and J. Neggers, “Derivations on ranked bigroupoids,” Applied Mathematics & Information Sciences. In press.
[8] Y. B. Jun, E. H. Roh, and G. Muhiuddin, “Generalized derivations on ranked bi-groupoids,” Knowledge-Based Systems. Under review process.
[9] Y. Huang, BCI-Algebra, Science Press, Beijing, China, 2006.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.