If the BCK-part of a BCI-algebra (X,$\cdot,0)$ is trivial, then $(X,+)$, where $x+y=x(Oy)$, is an abelian group. Conversely, if $(X,+)$ is an abelian group, then (X,$\cdot,O)$, where $xy=y-x$, is a BCI-algebra and its BCK-part is trivial.
Reviewer’s remark: This result was presented by the reviewer during the All-Polish Conference on Universal Algebra and its Applications, Opole, May 1985 (see Materiały or Demonstr. Math. (appear)).