REGULARITY OF GENERALIZED DERIVATIONS IN BCI-ALGEBRAS

Title & Authors
REGULARITY OF GENERALIZED DERIVATIONS IN BCI-ALGEBRAS
Muhiuddin, G.;

Abstract
In this paper we study the regularity of inside (or outside) ($\small{{\theta},{\phi}}$)-derivations in BCI-algebras X and prove that let $\small{d_{({\theta},{\phi})}:X{\rightarrow}X}$ be an inside ($\small{{\theta},{\phi}}$)-derivation of X. If there exists a $\small{{\alpha}{\in}X}$ such that $d_{({\theta},{\phi})}(x){\ast}{\theta}(a) Keywords BCI-algebra, regular inside (or outside) ($\small{{\theta}{\phi}}$)-derivation;$\small{{\theta}}$-ideal;$\small{{\phi}}$-ideal;invariant inside (or outside) ($\small{{\theta}{\phi})}$-derivation; Language English Cited by References 1. S. A. Bhatti, M. A. Chaudhry, and B. Ahmad, On classification of BCI-algebras, Math. Japon. 34 (1989), no. 6, 865-876. 2. M. A. Javed and M. Aslam, A note on f-derivations of BCIalgebras, Commun. Korean Math. Soc. 24 (2009), no. 3, 321-331. 3. Y. B. Jun and E. H. Roh, On the BCI-G part of BCI-algebras, Math. Japon. 38 (1993), no. 4, 697-702. 4. Y. B. Jun and X. L. Xin, On derivations of BCI-algebras, Inform. Sci. 159 (2004), no. 3-4, 167-176. 5. Y. B. Jun, X. L. Xin, and E. H. Roh, The role of atoms in BCI-algebras, Soochow J. Math. 30 (2004), no. 4, 491-506. 6. D. J. Meng, BCI-algebras and abelian groups, Math. Japon. 32 (1987), no. 5, 693-696. 7. G. Muhiuddin and A. M. Al-Roqi, On t-derivations of BCI-algebras, Abstr. Appl. Anal. 2012 (2012), Article ID 872784, 12 pages. 8. G. Muhiuddin and A. M. Al-Roqi, On (${\alpha},{\beta}$)-derivations in BCI-algebras, Discrete Dyn. Nat. Soc. 2012 (2012), Article ID 403209, 11 pages. 9. G. Muhiuddin and A. M. Al-Roqi, On left (${\theta},{\phi}\$)-derivations in BCI-algebras, J. Egyptian Math. Soc. 22 (2014), no. 2, 157-161.

10.
G. Muhiuddin and A. M. Al-Roqi, Generalizations of derivations in BCI-algebras, Appl. Math. Inf. Sci. 9 (2015), no. 1, 89-94.

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