The authors study BCI-algebras. The main contribution in this paper is the introduction of the notion of a derivation for BCI-algebras, which is defined in a way similar to the notion in ring theory. This is done by using the cap-operation and the BCI-product. Also, many properties related to the derivations are developed. In particular, the authors study the regular derivation in detail, they give a characterization of regular derivations and characterize the p-semisimple BCI-algebras. This is a quite intesting paper for those who study BCI-algebras.
Reviewer’s remark: The abelian group structure of a p-semisimple BCI-algebra was first given by T. D. Lei and the reviewer [Math. Jap. 30, 511–517 (1985; Zbl 0594.03047)], not in  of the references in the paper.