Abstract: We collect some important concepts on BCK,BCI and BCL-algebras which are useful to develop the main results in subsequent topics. The left-right m-derivation of a BCI-algebra is introduced, and some related properties are investigated. Using the idea of regular m-derivation , we give characterizations of a p-semi-simple BCI-algebra .We introduce the useful properties of m-derivation in BCI-algebras and commutative and maximal ideals in BCK-algebras .