Abstract
In this paper, by considering the notions of left-right and right-left derivations
of BCI-algebras, we generalize some results on regular derivations and classify
this derivation in P-semisimple BCI-algebra and BCK-algebra. Then we make a
congruence relation, for any derivation d of X and defined the concept of conjugate
derivations. In the sequel, we show that the set of all equivalence classes of X with
respect to this relation forms a BCI-algebra and we denote it by X/d. Finally, we get
some interesting result about these quotient algebras.
