REGULARITY OF GENERALIZED DERIVATIONS IN BCI-ALGEBRAS Muhiuddin, G.;
In this paper we study the regularity of inside (or outside) ()-derivations in BCI-algebras X and prove that let be an inside ()-derivation of X. If there exists a such that , then is regular for all . It is also shown that if X is a BCK-algebra, then every inside (or outside) ()-derivation of X is regular. Furthermore the concepts of -ideal, -ideal and invariant inside (or outside) ()-derivations of X are introduced and their related properties are investigated. Finally we obtain the following result: If is an outside ()-derivation of X, then is regular if and only if every -ideal of X is -invariant.